Effects of Tilt, Shade, and Temperature on Photovoltaic Panel Performance

Presented to the University of California, San Diego

Department of Mechanical and Aerospace Engineering MAE 126A

March 15, 2016

Prepared by

Justin Bosch Sik Cho Gene Lee

Robert Zhang

Group EE2 Wednesday AM

Abstract

Many different factors affect the maximum power output and efficiencies of photovoltaic

solar panels. This experiment was conducted to explore the effects of tilt, shading, and

temperature on PV panels. The solar altitude angle was measured on the shadow compass to be

38±3 degrees, which was used to calculate the optimal tilt angle of 52±3 degrees. At the 50

degree tilt measurement for the Kyocera solar panel, the maximum open circuit voltage of 19.3 ±

1.9 V, short circuit current of 0.75 ± 0.08 A, maximum power output of 10.06 ± 0.14 W, and

solar irradiance of 10000 ± 15 were found from the MP­170. The next set of/mW 2

measurements were to compare vertically and horizontally shading the cells in the grid of the

solar panel. The power output and efficiency graphs showed that horizontally shaded panel was

more likely to follow the trends of a typical I­V curve and have a more linear relationship

between the efficiency and shaded ratio than that of the vertically shaded. The last week of the

experiment was to observe the effect of temperature reduction on the PV panel. The

voltage­temperature coefficient was determined to be 0.062 . These coefficients along with/V

corrected power values were used to create a corrected efficiency plot that shows how the

panel’s efficiency increases by 0.076% per .

1

Table of Contents

List of Tables……………………………………………………………………………………... 3

List of Figures……………………………………………………………………………………..4

Introduction………………………………………………………………………………………..5

Theory……………………………………………………………………………………………..6

Experimental Procedure………………………………………………………………………...... 8

Data and Results…………………………………………………………………………………10

Discussion and Error Analysis……………………………………………………………...........16

Conclusion……………………………………………………………………………………..... 21

References……………………………………………………………………………………......23

Appendices and Raw Data……………………………………………………………………….24

2

List of Tables

Table Description Page

A Rated Specifications and Measured Values for KY and US Panels at 0 and 30 degrees

10

3

List of Figures

Figure Description Page

1 I­V Curves for Kyocera (KY) and Uni­Solar (US) PV Panels at 0 and 30 Degrees 9

2 Short Circuit Current ( ) vs. Tilt Angle (ᵯ)Isc 24

3 Open Circuit Voltage ( ) vs. Tilt Angle (ᵯ) V oc 25

4 Maximum Power Point Voltage vs. Global Irradiance in Plane of Panel 10

5 Maximum Power Point Power Output vs. Global Irradiance in Plane of Panel 10

6 I­V Curves for Vertically Shaded Cells 25

7 I­V Curves for Horizontally Shaded Cells 26

8 Panel Output Power as a Function of Load Voltage for Vertical Shading 10

9 Panel Output Power as a Function of Load Voltage for Horizontal Shading 10

10 Shaded/Unshaded Max Power Pt Power Ratio as Function of Shade Ratio w/ Vertically Shaded Linear Fit

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11 Shaded/Unshaded Max Power Pt Power Ratio as Function of Shade Ratio w/ Horizontally Shaded Linear Fit

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12 Reduction in Electrical Conversion Efficiency as a Function of Shaded Ratio w/ Vert Shaded Linear Fit

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13 Reduction in Electrical Conversion Efficiency as a Function of Shaded Ratio w/ Horiz Shaded Linear Fit

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14 Electrical Conversion Efficiency as a Function of Panel Temperature 26

15 Maximum Power Point as Function of Power Temperature 27

16 Voltage at the Maximum Power Point as a Function of Panel Temperature 13

17 Current at the Maximum Power Point as a Function of Panel Temperature 14

18 Current at Maximum Power Point as a Function of Panel Temperature with Linear Regression for Data Set 1

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19 Current at Maximum Power Point as a Function of Panel Temperature with Linear Regression for Data Set 2

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20 Corrected Electrical Conversion Efficiency relative to Panel Temperature for both data sets

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4

Introduction

With technology continuing to advance in an accelerated rate, the world looks at new and

improved ways to provide energy to this ever­so energy demanding world. As sustainable energy

technology becomes more prevalent, drawing energy from a renewable energy source, such as

the sun, has become popular method of providing energy to the world.

Photovoltaics (PV) is the name of a method of converting solar energy into direct current

electricity. Utilizing semiconductive materials, solar panels are employed in which solar cells

supply usable solar power. By exposing these solar panels to light, in this case the sun, the solar

cells are able to create voltage or electrical current, thereby providing the necessary energy for an

electric consuming technology. This process is also known as the photovoltaic effect. The

photoelectric effect was first noted by a French physicist, Edmund Bequerel in 1839, who found

that certamin materials would produce small amounts of electric current when exposed to light

(Reference 1). This experiment looks to study the different aspects of PV and how they can be

utilized to produce the maximum amount of energy.

Utilizing the sun to create energy seems almost too good to be true and poses the question

why it is not being utilized for every electric device. Utilizing solar PV, however, requires proper

conditions to be met in order to use it at its highest efficiency. This experiment also looks at how

the amount of sunlight can affect the solar panel’s efficiency as well as the effect of PV cell

temperature on the electrical conversion efficiency. By understanding how the PV solar panels

can be best utilized for maximum efficiency, solar energy systems can become a more utilized

option in producing zero­emissions and an environmentally sustainable energy solution for the

world.

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Theory

Photovoltaics use solar cells that convert photos from the sun into a flow of electrons.

Electrons are knocked loose from their atoms as they are excited, acting as charge carriers for an

electric current. Through an array of solar cells, they convert solar energy into a usable amount

of direct current electricity. Direct current allows the electric current to flow in a constant

direction, which can be used to charge batteries and as power supply for electronic systems. The

power of these PV devices can be determined by measuring the electric current (I) and voltage

(V) in a circuit.

VP = Isc oc (1)

The short circuit current is defined as the current that would flow in the closed circuit

while the open circuit voltage refers to the voltage drop across the circuit when no current flows

in the circuit. The power of the PV cell is also affected by the solar irradiance, which is the

energy coming from the sun. A high solar irradiance results in a high current, which ultimately

increases the power, or rate of energy, produced by the PV cell. The Global Horizontal

Irradiance (GHI) is the amount of terrestrial irradiance falling on a surface horizontal to the

surface of the Earth.

HI Direct Normal (DNI) cos(z) τ Diffuse Horizontal (DHI)G = * * + (2)

DNI refers to the the direct normal irradiance, which is the total amount of solar radiation

per unit that comes directly from the sun. DHI refers to the diffuse horizontal irradiance, which is

the total amount of solar radiation per unit area that has been scattered or diffused by the

atmosphere. The position of the sun relative to the an observer on the surface of the Earth is also

an important factor needed to model PV system performance. The solar zenith angle (z) is the

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angle between the zenith and the centre of the sun’s disc. In order to maximize irradiance, it is

important for the solar ray to be perpendicular to the solar panel. In equation (2), refers to theτ

ratio between outgoing and incoming sunlight and is called atmospheric transmissivity.

τ = DNIsourceDNI (sea level) (3)

The conversion efficiency of a PV panel is also important in modeling a PV system.

Equation (4) below describes the percentage of solar radiation incident on the panel that is

converted to electrical energy, and is usually listed for the maximum power point.

/ GI Aη = Pmpp POA (4)

Where is the power at the maximum power point on the I­V curve, is the incidentPmpp IG POA

irradiance in the same plane as the surface of the PV panel and A is the panel surface area.

Like other semiconductor devices, solar cells are sensitive to temperature. The

temperature coefficients of a panel can be determined through the following ratio:

TC = ΔTcellΔPcell (5)

Where the numerator refers to the change in power of a cell and the denominator refers to the

change in temperature of a cell. As the equation shows, the coefficients can be found through the

slope of the voltage vs temperature and current vs temperature data plots. Using Equation (6)

below, an estimation of the linearized current to irradiance coefficient can be found.

γ = ΔGHIΔIMPP (6)

7

Experimental Procedure

Week 1 Procedure

The first week, the experiment looked at using the basic functions of the EKO MP­170

Photovoltaic Module & Array Tester. First an inventory of all the cables and equipment was

taken. By locating a sunny spot in the EBU2 quad, both solar panels were placed next to each

other on the wooden board. With the MP­170 powered off, the black and red PV leads were

connected to the appropriate wires on one of the panels. The thermocouples were then connected

to the Sensor Unit, with one of the thermocouples placed in the shade. Next the solar zenith

angle was checked for using the compass with a picture of cross shadow taken for the report.

After making sure that everything was connected to its respective ports, using the Sensor Unit

the proper settings were set to make sure the panels would be reading proper data. At the home

screen, CONFIG > MEAS PAR > ENTER > SELECT > ENTER, highlighting the measurement

protocol from the PARAMETER LIST > ENTER. At home CONFIG > SYSTEM > ENTER>

highlight DATE & TIME SET > enter current time. At home, DATA > ERASE> ENTER>

ALL>enter current time. At home, MEASURE was pressed. Once the data was obtained for the

0° tilt angle, the same process was used for the 10°, 20°, 30°, 40°, 50°, and 60° tilt angle for only

one of the panels.

Week 2 Procedure

This second week looked to investigate the effect of shading the PV panel power output and

efficiency. Like Week 1, first an inventory of all of the equipment was taken to ensure

everything was there. Again by locating a sunny spot in EBU2, the 10W Unisolar PV panel was

placed flat on a surface and the MP­170 was setup for measurement. First a baseline performance

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measurement was taken when the panel was un­shaded. After, the panels were partially shaded

using the first column of cells on the panel in increments of two cells. Using a completely

opaque material, the cells were covered in the following order: (1,1); (1,1) through (3,1); (1,1)

through (5,1); (1,1) through (7,1); (1,1) through (9,1); (1,1) through (11,1). Then the panels were

shaded horizontally using the rows of cells on the panel. Again using a completely opaque

material, the cells were covered in the following order: Row 1, Row 1­2, Row1­3, Row 1­4,

Rows 1­5.

Week 3 Procedure

For Week 3, the effect of PV cell temperature on the electrical conversion efficiency of

the panel was sought. The general procedure for the operation and measurement with the

MP­170 was the same setup as Week 1 and Week 2. The 10W Unisolar PV panel was placed flat

on a surface in the sun and the MP­170 was set up to take measurements. One measurement of

the I­V curve was taken to ensure that everything was set up correctly. A plastic bag was filled

with ice then used to cover the entire surface of the PV panel to allow the panel to cool for

approximately 10­15 minutes. The bag of ice was then removed and measurements were taken.

The initial temperature readings were around 8 or 9 degrees and we took data readings until the

temperature rose to about 50 degrees, where the temperature was close to steady state. Numerous

measurements were taken as frequently as possible before the panel reached steady state. The

goal of this procedure was to measure the I­V curve of the panel at several different panel

temperatures. After the panel reached steady state, the steps in covering the panel with ice and

taking measurements were repeated to have two complete sets of measurements, waiting 5­10

minutes between the two tests.

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Data and Results

Week 1 Data

Figure (1) I­V Curves for Kyocera (KY) and Uni­Solar (US) PV Panels at 0 and 30 Degrees

(W)Pmax (V)V max (A)Imax

US Specifications 10.3 16.5 0.62

US at 0 degrees 6.68 15.0 0.45

US at 30 degrees 9.72 14.9 0.65

KY Specifications 10 17.4 0.58

KY at 0 degrees 6.2 15.3 0.41

KY at 30 degrees 9.4 15.2 0.62 Table (A) Rated Specifications and Measured Values for KY and US Panels at 0 and 30 degrees

The two highest I­V curves in Figure 1 show that both the KY and US panels are both

more consistent with their rated performances at 30 degrees (as seen in Table 1) but are still

slightly under the maximum values.

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Figure (4) Maximum Power Point Voltage vs. Global Irradiance in Plane of Panel Figure (5) Maximum Power Point Power Output vs. Global Irradiance in Plane of Panel

The maximum panel power output power of 10.06 W occurs at a 50 degree tilt with solar

irradiance of 1000 ./mW 2

Week 2 Data

Figure (8) Panel Output Power as a Function of Load Voltage for Vertical Shading Figure (9) Panel Output Power as a Function of Load Voltage for Horizontal Shading

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As seen in Figure (8), the power output curves all have relatively different shapes but all

uniformly reach 0 around 20 volts . For the horizontally shaded data in Figure (9), the curves are

relatively proportional but have different voltage ranges depending on the amount of cells

covered in the grid of the panel. However, the amount of cells shaded appear to have the same

effect on the maximum amount of power for both horizontal and vertical shading.

Figure (10) Shaded/Unshaded Max Power Pt Power Ratio as Function of Shade Ratio w/ Vertically Shaded Linear Fit Figure (11) Shaded/Unshaded Max Power Pt Power Ratio as Function of Shade Ratio w/ Horizontally Shaded Linear Fit

Comparison of Figures (10) and (11) shows that the horizontally shaded data fits the

linear regression best. However, it also shows that as the shaded area ratio increases, the

maximum power ratio of horizontal shading decreases significantly faster than that of vertical

shading.

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Figure (12) Reduction in Electrical Conversion Efficiency as a Function of Shaded Ratio w/ Vert Shaded Linear Fit Figure (13) Reduction in Electrical Conversion Efficiency as a Function of Shaded Ratio w/ Horiz Shaded Linear Fit

From comparison of Figures (12) and (13), it is clear that the horizontally shaded data fits

the linear regression best. Figures (10), (11), (12), and (13) clearly show proportional

relationship between the shaded and unshaded maximum power point power ratio and electrical

conversion efficiency as the graphs look almost identical. Figures (12) and (13) also show that

when the shaded ratio is less than about 0.3, the horizontal shade gives a better efficiency and

vice versa.

Week 3 Data Figures (14) and (15) in the Appendix appear to have decreasing trends but the minimum

temperature measurements have outliers that say the maximum power output and efficiency are around 0,

causing the linear fit to have a positive slope. This discrepancy continues throughout the rest of the graphs

for week 3. The GHI and efficiency appear to have an inverse relationship as the GHI values get higher

for lower efficiencies.

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Figure (16) Voltage at the Maximum Power Point as a Function of Panel Temperature

Figure (17) Current at the Maximum Power Point as a Function of Panel Temperature

The voltage­temperature coefficient was found to be 0.062 , which is way off from/V

the rated value of ­0.0027 . and GHI appear to have a slightly negative relationship,/V V MPP

while and GHI have a slightly positive relationship.IMPP

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Figure (18) Current at Maximum Power Point as a Function of Panel Temperature with Linear Regression for Data Set 1 Figure (19) Current at Maximum Power Point as a Function of Panel Temperature with Linear Regression for Data Set 2

The linear regression functions for each data set was used to compute the linearized

to GHI coefficient of . The current­temperature coefficient wasIMPP .92248 0γ = − 1 × 1 −4WA•m2

then calculated to be 0.0084. Notable information: Increasing the temperature reduces the band

gap by increasing the energy of the electrons. This causes the I_sc to increase slightly and the

V_oc to decrease.

Figure (20) Corrected Electrical Conversion Efficiency relative to Panel Temperature for both data sets

The Figure above shows that the efficiency increases 0.076% per degree C.

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Discussion and Error Analysis

Week 1

The objective of the full experiment was to study the reliability and efficiency of solar

panels using two different models of panels, based on three varying conditions: tilt, shading, and

temperature. The first week, we tested the solar panels’ capability based on tilt angle.

During the first week of the experiment, the major systematic error that the data were

subject to was the tilt angle, since it was the only values measured manually. It is safe to give an

error of for each trial. Based on the readings at 0 and 30 degrees for both the US and KY ± 2 °

panel, the short circuit currents and the open circuit voltages were found at each angle. At 0

degrees tilt, the short circuit current for the US panel was 0.45A (45% error from specifications)

and the open circuit voltage was 15.0V (9.09% error). At 30 degrees, the values were 0.65A

(4.84% error) and 14.9V (9.70% error). For the KY panel, the values were 0.41A (29.31% error)

and 15.3V (12.07% error) at 0 degrees tilt, and 0.62A (6.90% error) and 15.2V (12.64% error) at

30 degrees tilt. Based on this data, two definite conclusions can be made. First, the short circuit

currents for both panels at 30 degrees tilt were greater than the given specification values

(104.8% efficiency for US and 106.9% efficiency for KY). Therefore, we can conclude that the

readings are not fully accurate and that there are some systematic errors that we cannot control.

However, the I­V curves at 30 degrees were relatively consistent with the rated performances of

the PV panel because 30 degrees is a more optimal angle to catch total irradiance along with the

only slightly cloudy weather that brought the values close to their maximum rated specifications.

Secondly, the readings show that the short circuit current changes significantly with angle, but

the open circuit voltage stays relatively constant, regardless of tilt angle.

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The maximum power was achieved at a 50 degree tilt angle, as highlighted in Figure 5.

The geographic and astronomical significance of this angle is that maximum power is achieved

when the direct normal irradiance (DNI) is perpendicular to the surface of the panel, which

occurs at the complementary angle of the solar altitude angle (ALT or angle from the horizon to

the sun’s center). At 9:26AM, the ALT was 34 degrees as seen in Figure A, but by the time the

tilt angle was changed to 50 degrees at 9:44AM, the sun may have risen to an amount closer to

40 degrees, the complementary angle of the ALT. The maximum power point on is located at

where the curve begins to get steeper or where the current begins to drop more rapidly as the

voltage goes up.

The MP­170 solar sensor unit has a measurement limitation which gives a error of%± 1

current and voltage readings and a error for solar irradiance readings. Since the values of.5%± 1

current and voltage are used to calculate the max power, the limitations also attribute to the error

in the measured value of power

0.06 .14 W δPmax = Pmax√0.01 .012 + 0 2⇒ Pmax = 1 ± 0

I .015 I 000 5 δGI = G × 0 ⇒ G = 1 ± 1 Wm2

*GI = global irradiance

Week 2

The second week, we studied the effect of shading on the production of the solar panels.

For week 2, we studied only the US solar panel. It is safe to say that this part of the experiment

had a very small, maybe , error in the tilt angle because the whole experiment was at a 0± 1°

degree tilt and was never changed.

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As seen in Figures 6, 7, 8, and 9, the shaded and unshaded maximum power point ratio

and electrical conversion efficiency for vertical shading per shaded ratio first drops dramatically

and then levels into a more linear data set, while the horizontal shading has a more linear trend

throughout and thus fits the linear regression better. Reasons for these different trends can be

because vertical shading may hinder the unidirectional flow of the direct current throughout the

panel. The large jump between the first and second point in the vertical shading might be

because shading just one cell may be exponentially weaker than covering two or more at a time.

Our results imply that the different I­V curves and maximum power points from the

shaded and unshaded points make affects the inverter when converting the DC to AC. The

maximum power point tracking is thrown off since the inverter cannot choose an optimum

voltage for all cells, especially for vertical shading with unproportional and unpredictable power

curves. Some cells produce much less power than they could under their maximum power point

voltage, and the power loss in partial shading is disproportionately large compared to the fraction

of the shaded area.

Week 3

The third week, we studied the effect of temperature change on the production of the

solar panels. For this week, we studied only the US solar panel. It is, again, safe to say that this

part of the experiment had a very small, maybe , error in the tilt angle because the whole± 1°

experiment was at a 0 degree tilt and was never changed.

Based on the data readings as the temperature of the panel increases, the higher the global

horizontal irradiance (GHI) values are, the efficiency unexpectedly gets lower. However, as seen

in Figures 14 and 15, because of a few outlier points at the lower temperature readings, the best

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fit line is still positive. This is because as the time of the measurements advanced later into the

morning, the sun rose higher in the sky, causing the GHI to go up. The only explanation for

lower efficiencies with a higher GHI in the context of this experiment is that the lower

temperature overpowers the amount of a higher GHI on the efficiency of the panel.

The calculated voltage­temperature coefficient of 0.062 , which is simply the slope/V

of the linear fits, was not even the same sign as the rated value of ­0.0027 (/V .06470

discrepancy : 2396.3% error). Even though most of the data looks like it has a negative trend, the

minimum temperature of each data set have outlying values so low that the calculated linear fit

has a positive slope, as seen Figure 16. These outliers may exist because the panel was not dry

enough after removing the ice, causing water on the surface to diffract the irradiance.

On a typical I­V curve, the current increases as the voltage decreases. The negative

relationship of and GHI and positive relationship and GHI proves that when theV MPP IMPP

power decreases, whether it be from GHI or temperature in this case, either voltage or current

increases and the other has to decrease to stabilize at the new maximum power point on each I­V

curve. The average GHI for the first trial was 823.0347 W/m2 and for the second trial, 952.2032

W/m2, with an error related to the MP­170’s limitation in measure solar irradiance and the

number of trials. The noticeable increase in the average is most likely due to the fact that in the

span over the two trials, the intensity of the sun increased significantly because the sun continued

to rise in the morning. Ignoring the linear fit, Figures 16 and 17 visibly showed that voltage

decreased as current increased.

.416%δ GHI = √n1.5% = √13

1.5% = 0

Trial 1 Average GHI 23= 8 ± 3Wm2

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Trial 2 Average GHI 52= 9 ± 4Wm2

GHI 129Δ = ± 5Wm2

The average maximum power currents were also determined by fitting a best fit line to the data

set, which was 0.5293A for trial 1 and 0.5045A for trial 2. The error in these values also come

from the MP­170’s limitation in measuring current and the number of trials.

.277%δIMPP = √n1.0% = √13

1.0% = 0

Trial 1 Average .5293 .0015 AIMPP = 0 ± 0

Trial 2 Average .5045 .0014 AIMPP = 0 ± 0

I .0248 .002AΔ MPP = − 0 ± 0

Note that the change in GHI from trial 1 to 2 is a significant positive change, while the change in

IMPP from trial 1 to 2 is a slight negative change. This shows that GHI and maximum power

currents are inversely proportional.

.92248 0γ = ΔGHIΔIMPP = 129W

m2

−0.0248A = − 1 × 1 −4WA•m2

.92248 0 .17 0 δγ = − 1 × 1 −4√( 5129)

2 + ( 0.0020.0248)2 = 0 × 1 −4

WA•m2

1.92 .17) 0γ = ( ± 0 × 1 −4WA•m2

Finally, we plotted and calculated the corrected electrical conversion efficiency to determine the

effect of temperature on the panel’s efficiency. It was determined that the panel’s efficiency

increases 0.076% per every degree Celsius.

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Conclusion

In an ever so energy demanding world, new forms of energy are always being looked

into. For the past centuries, the world has relied on mainly non­renewable resources to provide

energy. With increasing demand for energy and the increasing rate of greenhouse emission being

produced every year, new and renewable energy solutions are being sought out. Solar energy

using photovoltaics stands as a clean and renewable source of energy. Using the sun’s energy,

which seems like an inexhaustible source of energy, seems like a promising solution. Utilizing

photovoltaics, however, can be complicated and has many factors that play a part in producing

energy efficiently. This experiment examined how some of these factors play a role in converting

solar energy into usable energy.

Three factors that were analyzed was the solar panel tilt angle, partial shading, and

temperature. After collecting data with a solar panel at various angles, the experiment showed

that the panel produced the maximum power output at an angle of 50 degrees. At this angle, the

highest open circuit voltage Voc , short circuit current I sc , maximum power output Pmpp , and

incident irradiance GHI were recorded. Next data was collected by shading parts of the solar

panel and seeing how it affected its results. As predicted, the experiment showed that the shaded

and unshaded maximum power point ratio and electrical conversion efficiency for vertical

shading per shaded ratio first drops dramatically and then levels into a more linear data set, while

the horizontal shading has a more linear trend throughout and thus fits the linear regression

better. Lastly, the the effect of temperature on the solar panels was analyzed. Through the data,

the experiment showed that as the temperature increased, the voltage decreased. This can be seen

with a negative voltage­temperature coefficient, ­0.0027 . Finally, we plotted and/V

21

calculated the corrected electrical conversion efficiency to determine the effect of temperature on

the panel’s efficiency. It was determined that the panel’s efficiency increases 0.076% per every

degree Celsius.

In conclusion, this experiment showed that in order to maximize a solar panel’s

efficiency in producing usable energy, many factors need to be accounted for. The sun may seem

and act as a renewable energy that is constantly hitting the Earth. But in order to convert the

solar energy into usable energy that can be used in this world, much more development need to

take place for solar panels. By understanding how photovoltaics works and continuing to do

research, creating a more sustainable and cost efficient solar panel can one day play a bigger role

in helping to create a more sustainable future.

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References

1. Kleissl, J., Garai, A. “Solar Energy Systems”. UCSD Department of Mechanical and

Aerospace Engineering. March 2016.

https://sites.google.com/a/eng.ucsd.edu/mae­171a­175a­126a/solar­pv

2. Kleissl, J., Garai, A. “Solar PV Lecture”. UCSD Department of Mechanical and Aerospace

Engineering. March 2016.

https://sites.google.com/a/eng.ucsd.edu/mae­171a­175a­126a/solar­pv

3. Knier, Gil. “How do Photovoltaics Work?”. NASA. March 2016.

http://science.nasa.gov/science­news/science­at­nasa/2002/solarcells/

4. Photovoltaic Education Network. March 2016. http://pveducation.org/

5. Skoplaki, E., Palyvos, J.A. “On the temperature dependence of photovoltaic module

electrical performance: A review of efficiency/power correlations.” Solar Engineering Unit,

School of Chemical Engineering, National Technical University of Athens. 14 October

2008. http://ac.elscdn.com

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Appendices and Raw Data

Figure A: Solar Altitude Angle for Week 1

Figure B: Solar Altitude Angle for Week 2

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Figure C: Solar Altitude Angle for Week 3

Figure 2: Short Circuit Current ( ) vs. Tilt Angle (ᵯ)Isc

25

Figure 3: Open Circuit Voltage ( ) vs. Tilt Angle (ᵯ)V oc

Figure 6: I­V Curves for Vertically Shaded Cells

26

Figure 7: I­V Curves for Horizontally Shaded Cells

Figure 14: Electrical Conversion Efficiency as a Function of Panel Temperature

27

Figure 15: Maximum Power Point as Function of Power Temperature Matlab Code

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