An experiment to measure the efficiency of a photovoltaic module due to tilt angle, shading, and temperature

February 28, 2012Priscilla Camanho, Peter Chiu, John Chung-Sang Lee, Kevin J WongEnvironmental Engineering, Mechanical and Aerospace Engineering, University of California San Diego, San Diego, California, 92093

Abstract

Factors that affect the efficiency of a solar panel are tested in this experiment to understand

how one should install solar modules for maximum efficiency. As the tilt angle was increased from 0

degrees, the efficiency of the solar panel rises until it hits 50 +/- 1 degrees at which the maximum

efficiency is reached. This most efficient angle is dependent upon the geographic location of panel as

well as the time of the day and is where the solar arrays are shining perpendicular to the solar panels.

When testing the effect of shading on the solar panel, the results were inconclusive between whether

horizontal shading or vertical shading was more efficient. The horizontal shading showed a linear

relationship between efficiency and power output while the vertical shading showed less of a linear

relationship. This conclusion is due to the fluctuation in irradiance during the time of experiment as well

as the circuit properties which are not known. Lastly, the temperature showed a negative relationship

with the efficiency of the solar panel. As the temperature increased, the efficiency would decrease. The

current-temperature coefficient for test #1 and #2 were 0.00078 A/degC and 0.00066 A/degC,

respectively which had an error of 19.7% and 6.001%, respectively. These showed that the measured

data had results similar to the rated performances.

ContentsSubject Page I. Introduction ..............................................................................................................................................3II. Theory.................................................................................................................................................…3-5III. Experimental Procedure.......................................................................................................................5-7IV. Results ...............................................................................................................................................8-15V. Discussion .........................................................................................................................................15-19VI. Conclusion .......................................................................................................................................19-20VII. References…………………………………………………………………………………………………………………………………….…20

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I. Introduction

Increasing anthropogenic impact on the environment has led scientists and engineers to look for

more sustainable solutions for energy. A potential option is in the solar energy field, where generators

can produce electricity through solar energy. Photovoltaic cells are a type of generator that absorbs

photons of light and release electrons that can form an electric current and be used as electricity.

Investigating photovoltaic cells in a laboratory can help test the feasibility of using solar energy as a

sustainable source of energy as well as optimize a PV cell’s efficiency and use.

The objective of this experiment was to study aspects of PV performance conducive for the

design and implementation of solar PV power plants. The first aspect of the PV panels studied was

investigating the tilt angle of the panels and how it affected the power output of the panel. This was

done for two panels with a more varied testing of angles for the second panel. The second part of the

experiment tested the effect of shading on the PV panel’s electrical performance and efficiency. Finally,

the effects of cooling the PV panel are investigated and the voltage and current-temperature

coefficients are measured.

II. Theory

In order to discuss the efficiency of a solar panel, we need to establish some definitions. Firstly,

the power generated by a photovoltaic system is dependent on the current and the voltage which can

be determined using Equation 1.

Power = Current * Voltage or P = IV (1)

Figure 1 shows this relationship in which Isc is the short circuit current while VOC is the open circuit

voltage.

Solar panel efficiency can be determined by Equation 2 where Pmpp represents the maximum

power, Irr represents the irradiance, and A represents the surface area of the panel.

3

η=PmppIrr∗A

(2)

The solar irradiance and the production of the electricity from a photovoltaic system are directly

proportional. This means that as the solar irradiance increase, the solar panel’s power production

increases as well. However, the global horizontal irradiation (GHI) is the irradiance that is actually being

absorbed by the photovoltaic cells. The GHI is a factor of both angle and diffusivity of the solar

irradiance and is expressed by Equation 3.

GHI = cosine(SZA)*(T) + (diffused light) (3)

Figure 2 illustrates the SZA (solar zenith angle) in three dimensions. “T” is the atmospheric

transmissivity and is provided in Equation 4.

TDirect Normal Irradiation(at sealevel)

Direct Normal Irradiation(at sourcebefore hitting the atmospher) (4)

The efficiency of the solar panel is also depended on the tilt of the solar panel. During a sunny

day, the solar panel becomes more efficient as the sun rises until the solar array is perpendicular to the

solar panel and then the efficiency drops until the arrays do not reach the panel. As for the solar zenith

angle, the efficiency also changes depending on the location of the solar panel. North of the equator, the

panels should be tilted and pointing south so that an optimal angle is reached to reach the maximum

efficiency of the solar panel.

Shading on a solar panel affects the efficiency as well. Ideally, the percentage of area shaded

should reflect the percentage of power output (i.e. 5% area shaded means 5% less power output). In

4

Figure 1. I-V Curve Figure 2. Angle Illustration

reality, however, this may not be true and a small area shaded could lead to an even smaller power

output. This may be due to the inverter inefficiently adjusting for the

optimal current and voltage with shaded cells, since shaded cells have

a different I-V curve. It can also be affected by the orientation of the

shading (whether is vertical or horizontal).

Lastly, the temperature of a solar panel can also change the

efficiency of the solar panel. The higher the temperature, the more it shifts the I-V and P-V curve toward

the origin leading to lower efficiency. This is illustrated in Figure 3.

Since there will be two different sets of data that will be

gathered from this part of the experiment (temperature of the solar panel versus the efficiency), a

corrected power will need to be used which is Equation 5.

PowerMPP−Corrected=CurrentMPP−Corrected∗V MPP−Measured (5)

The corrected current will follow Equation 6 which requires gamma from Equation 7.

CurrentMPP−Corrected=CurrentMPP−Measured+γ∗(GHIAverage−GHI ) (6)

γ=CurrentMPP−MeasuredAverage¿ 1−CurrentMPP−Measured

Average ¿ 2¿ ¿GHI 1−GHI 2

(7)

III. Experimental Procedure

The equipment used in this experiment was as follows:

EKO Mp-170 Photovoltaic Module & Array Tester Unisolar and Kyocera PV Panels Power Supply Grounding cable PV Leads Rs-485 cable for sensor unit Thermocouple wires

5

Figure 3. I-V and P-V curve as Temperature Changes

Using the PV leads, the Unisolar and Kyocera PV panels were individually connected to the MP-170. This

formed the basis of all measurements taken, along with implementing individual effects to the panel.

The data was subsequently transferred to a computer via the MP-170 Control Program.

Connecting the PV Panel and MP-170

Both the Unisolar and Kyocera PV panels were placed next to each other on a flat surface

exposed to the sun. The black and red PV leads connected from one the PV panels to the MP-170. The

thermocouple wires connected to the ports on the back of the sensor panel labeled “Temp 1” and

“Temp 2”. “Temp 1” connected to the back of the PV panel and “Temp 2” was placed in the shade to

measure the air temperature. The sensor unit was then connected to the MP-170, which was now

grounded. To ensure that the panel and the pyranometer were on the same plane to the sun, the

shadow compass device on the sensor unit was aligned by placing the compass on the panel and then

matching the shadow locations when it was placed back on the sensor unit. After grounding the MP-170,

measurements were ready to be taken. Measurement parameters were adjusted and ready to be taken

by the MP-170.

PV Panel Performance and Tilt

The PV panels were each measured at specific tilt angles, first 0o then 30o. The panel was tilted

by utilizing wooden blocks and adjusting for the correct angle. After measuring both panels, more varied

angles for the Kyocera panel were used. Angles of 0o,10o, 30o,40o,50o,60o were used. After completing

each measurement, the data from the MP-170 was uploaded to a computer using the Control Program

software.

Effect of Shading on PV Panel Performance

Next, the effects of shading different portions of the panel on power output and efficiency were

investigated. After following the previous procedure for connecting the PV panel and MP-170,

6

measurements were ready to be made again. The 10 W Unisolar PV panel was placed on a flat surface;

the general layout of the panel is shown in Figure 4.

The cells on the panel were labeled according to standard matrix

notation. The first measurement was taken with the panel un-shaded. Next,

the panels were shaded both vertically and horizontally. It was shaded

vertically by covering the first column of cells in increments of two cells. For

example, referring to figure 1, the (1,1) cell was covered and measured, then

the (1,1) through (3,1) cells were covered until the (11,1) cell was reached.

Next, to shade the cells horizontally, the first row (cells (1,1) and (1,2)) were covered and

measured. Rows 1 and 2 were measured next, and then Rows 1 through 3, adding a row between each

measurement until the fifth row was reached. After collecting all our measurements, the data was

uploaded to a computer.

Effect of PV Cell Temperature on the Electrical Conversion Efficiency

The last effect on the PV Panel was the cell temperature on the electrical efficiency. This effect

was implemented by taking a bag of ice and cooling the panel, investigating the efficiency changes

according to temperature. The 10W Unisolar PV was first placed out under the sun and the MP-170

turned on and connected.

A bag of ice was placed on top of the panel, covering the entire surface for about 10 minutes.

After removing the bag of ice and drying the panel surface, the measurements were taken with the MP-

170. Measurements were taken as frequently until the panel reached a steady state temperature,

around 40oC. A note of importance was that there were some delays between each measurement to

prevent overheating of the MP-170 device. After the panel reached steady state, the procedure was

repeated and measurements were taken once again to collect 2 data sets.

7

Figure 4. General layout of Unisolar PV Panel

IV. Results

Effect of Tilt Angle on PV Panel Performance

The Unisolar and Kyocera solar panels were measured at a tilt angle of 0 and 30 degrees each.

Figure 5 shows the I-V curve of each panel at each tilt angle.

0 5 10 15 20 250

0.10.20.30.40.50.60.70.80.9

I-V Curve for Each Panel at 0 and 30 degreesunisolar 0 degrees

Unisolar 30 degrees

kyo 0 degrees

kyo 30 degrees

V (voltage)

I (Am

ps)

Figure 5. I-V Curve for Unisolar and Kyocera brand PV panels at 0 and 30 degrees

The next set of measurements in the experiment dealt with measuring only the performance

Kyocera solar panel while varying its tilt angle. In Figures 6 and 7 the short circuit current and the open

circuit voltage data are plotted against the tilt angle to show a rather linear relationship.

0 10 20 30 40 50 600.4

0.450.5

0.550.6

0.650.7

0.75f(x) = 0.00427072857142857 x + 0.478870428571429R² = 0.953128050517435

Alpha Versus Isc

Tilt Angle (alpha)

Isc (A

)

Figure 6 Short Circuit Current relationship with Angle

0 10 20 30 40 50 60 7019.6

19.8

20

20.2

20.4

20.6f(x) = 0.00616742919254657 x + 20.164868242236R² = 0.555939690024666

Alpha versus Voc

Tilt Angle (alpha)

Voc (

V)

Figure 7 Open Circuit Voltage relationship with Angle

With the angle changing, the global irradiance changes depending on the angle. Figures 8 and 9

shows the relationship between the maximum voltage and maximum power versus the irradiance.

8

600 650 700 750 800 850 900 950 100015.215.415.615.8

1616.216.416.6

f(x) = 0.00084702340589717 x + 15.4961154433216R² = 0.208502314199418

Voltage Max

Irradiance (GIPOA) [W/m^2]

Volta

ge (V

mpp

) [V]

Figure 8 Voltage Maximum relationship with Irradiance

600 800 10006789

1011

f(x) = 0.0106867702555348 x − 0.316529742832536R² = 0.971588987267708

Power Max

Irradiance (GIPOA) [W/m^2]

Pow

er o

utpu

t(Pm

pp) [

W]

Figure 9 Max Power Output relationship with Irradiance

The star at each plot represents the absolute maximum power output of the total data set.

Effect of Shading on PV Panel Performance

The current (I) in respect to voltage (V) was plotted with various degrees of shading as shown in

Figure 10 for vertical shading and Figure 11 for horizontal shading.

Figure 10. I-V Curve for vertical shading measurements.Figure 11. I-V Curve for horizontal shading measurements.

Similarly, the panel power was plotted as a function of voltage for vertical and horizontal shading as shown in Figure 12 and Figure 13 respectively.

9

Figure 12. P-V Curve for vertical shading measurements. Figure 13. P-V Curve for vertical shading measurements.

The ratio of the power at the maximum power point (Pmpp) of the shaded panel divided by the

un-shaded Pmpp was plotted as a function of the ratio of shaded area to total panel area for both vertical

and horizontal shading as shown in Figure 14 and Figure 15 respectively.

0 0.1 0.2 0.3 0.4 0.5 0.60

0.5

1

1.5

R² = 0.137328077581381

Vertical Shading

Shaded Area/Total Area

Pmpp

sha

ded/

Pmpp

uns

hade

d

Figure 14. The ratio of the max power for shade to unshaded panels as a function of the ratio of the shaded to unshaded area for vertical shading measurements.

0 0.1 0.2 0.3 0.4 0.50

0.050.1

0.150.2

0.25

R² = 0.797205363113251

Horizontal Shading

Shaded Area/Total Area

Pmpp

sha

ded/

Pmpp

uns

hade

d

Figure 15. The ratio of the max power for shade to unshaded panels as a function of the ratio of the shaded to unshaded area for horizontal shading measurements.

The reduction in electrical conversion efficiency (η) was plotted as a function of the ratio of the

shaded area to total panel area as shown in Figure 16 and Figure 17 for vertical and horizontal shading

respectively.

10

3 4 5 6 7 8 90

0.2

0.4

0.6

R² = 0.675990550996163

Vertical Shading

η [%]

Shad

ed

/Un

shad

ed

A

rea

Figure 16. The ratio of the shaded to unshaded area as a function of the panel efficiency for vertical shading measurements.

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 70

0.10.20.30.40.5

R² = 0.995135247806037

Horizontal Shading

η [%]

Shad

ed/U

nsha

ded

Are

a

Figure 17. The ratio of the shaded to unshaded area as a function of the panel efficiency for vertical shading measurements.

Effect of Temperature on PV Panel Performance

The relationship between electrical conversion efficiency and panel temperature for each test is

shown in Figures 18 and 19.

Figure 18. Plot of efficiency as a function of temperature for test #1

Figure 19. Plot of the efficiency as a function of temperature for test #2.

The linear relationship between the power output at the maximum power points and the

temperature of the solar panel for test#1 and test #2 is demonstrated in Figures 20 and 21 respectively.

Figure 20. Plot of power as a function of the temperature for test #1.

Figure 21. Plot of power and a function of temperature for test #2.

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Plotting the voltage as a function of the panel temperature generated a voltage – temperature

coefficient which was the slope of the line. The voltage- temperature coefficient for test #1 was found

to be –0.06019 V/degC and -0.06131 V/degC for test#2 as shown in Figures 22 and 23 respectively.

Figure 22. Plot of voltage as a function of temperature for test #1.

Figure 23. Plot of voltage as a function of temperature for test #2.

The current-temperature coefficient for test#1 was found to be 0.00044 A/degC and 0.00028

A/degC for test #2 as shown in Figures 24 and 25.

Figure 24. Plot of current as a function of temperature for test #1.

Figure 25. Plot of current as a function of temperature for test #2.

The average of the GHI value for test #1 was calculated to be 746.955 W/m2 and for test #2 was

729.224 W/m2. The GHI was found to be 17.73099 W/m2.

Using the data collected for both tests, a single plot was generated so the relationship between

the current and the panel temperature for test #1 and test #2 could be analyzed in more detail. The

slope of the lines was found to be 0.00044 A/degC for test #1 and 0.00028 A/degC for test #2.

12

5 10 15 20 25 30 35 40 450.45

0.46

0.47

0.48

0.49

0.5

0.51

0.52

0.53

f(x) = 0.000436908799481146 x + 0.496277460030752R² = 0.386330263592547

f(x) = 0.000284040342406708 x + 0.479877157042727R² = 0.157678175685331

Current vs Temperature

Test #2Linear (Test #2)Test #1Linear (Test #1)

T[degree C]

Impp

[A]

Figure 26. Plot of the current as a function of the panel temperature for both test #1 and test #2.

The average values for the current at the maximum power was found to be for test #1 0.508498

A and for test #2 0.48822 A. The Impp was calculated as 0.0202773 A.

The linearized Impp to GHI coefficient was calculated to be 0.001144 Am2/W and the corrected

current at the max power Impp was calculated for measurements for both tests as shown on Table 1.

Test #1 Test #2Corrected Impp (A) Corrected Impp (A)

0.492270718 0.4720144450.496427576 0.4798647660.514139576 0.4961092530.511287385 0.4839643530.509758797 0.4873063530.508656603 0.4879087930.519961287 0.4995457220.515479925 0.498688722

0.488581336Table 1. Calculated corrected current values for test #1 and test #2.

The corrected current-temperature coefficient was found by plotting the corrected Impp as a

function of the panel temperature. For test #1 the corrected current-temperature coefficient was found

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to be 0.00078 A/degC and for test #2 was 0.00066A/degC. Figures 27 and 28 show the linear

relationship between the corrected current value and the temperature of the solar panel.

10 15 20 25 30 35 40 450.470.480.49

0.50.510.520.53

f(x) = 0.000783129575526 x + 0.486593687000615R² = 0.693686710624494

Impp Corrected vs Temperature test #1

Series2Linear (Series2)Linear (Series2)T [degree C]

Impp

[A]

Figure 27. Plot of the Impp corrected as a function of the temperature of the panel for test #1.

5 10 15 20 25 30 35 40 450.450.460.470.480.49

0.50.51

f(x) = 0.000657511343481 x + 0.468906940772677R² = 0.545076014382317

Impp Corrected vs Temperaturetest #2

Series2Linear (Series2)T [degree C]

Impp

[A]

Figure 28. Plot of the Impp corrected as a function of temperature of the panel for test #2.

The corrected maximum power and the corrected electrical conversion efficiency are shown in

Table 2.

Test #1 Test #1 Test #2 Test #2Corrected Pmpp (W) Corrected (%) Corrected Pmpp (W) Corrected (%)

9.085822 7.90608 8.861831 7.9220279.097492 7.981143 8.818149 7.9145469.056703 7.945359 8.654078 7.7525088.949768 7.867681 8.556868 7.6727338.848502 7.785921 8.480873 7.6045898.816552 7.763612 8.501194 7.6592758.684912 7.637701 8.459728 7.6541428.654227 7.650733 8.367298 7.570514

8.328224 7.556953Table 2. Results of the calculated corrected Power and corrected efficiency.

The corrected electrical efficiency value was plotted as function of the temperature of the panel

for both test 1 and 2 as shown in Figures 29 and 30 respectively.

14

10 15 20 25 30 35 40 457.47.67.8

88.2

f(x) = − 0.0114264097268521 x + 8.13687402880716R² = 0.792093004798757

Efficiency vs TemperatureTest #1

Series2Linear (Series2)T[degree C]

efficie

ncy

[%]

Figure 29. Relationship between the corrected electrical converted efficiency and the panel temperature for test #1.

5 10 15 20 25 30 35 40 457.3

7.5

7.7

7.9f(x) = − 0.0127459145370435 x + 8.07520304578268R² = 0.896414697663014

Efficiency vs temperaturetest #2

Series2

Linear (Series2)

T [degree C]

efficie

ncy

[%]

Figure 30. Relationship between the corrected electrical converted efficiency and the panel temperature for test #2.

V. Discussion

Effect of Tilt Angle on PV Panel Performance

The rated performance of the Uni-solar solar panel was rated at 1kW/m2. With this setting, the

short circuit current and the open circuit voltage were 0.78A and 23.8V respectively which is not the

same as the measured data at 0 degrees (a difference of about 34% and 9%) and is close to the data at

30 degrees (a difference of about 1% and 7%). For the Kyocera solar panel, the rated performances were

rated at 1kW/m2 as well. The short circuit current and the open circuit voltage were 0.62A and 21.7V

respectively which was not the same as the measured data at 0 degrees (a difference of about 24% and

10%) and is again, close to the data at 30 degrees (a difference of about 38% and 1%). The difference

would be due to the fact that the irradiance measured was less than 1kW/m2 which means that the solar

panels were not able to produce the full amount of power. Temperature might have had an effect as

well. If it was higher than 25 Celsius, then the efficiency might have dropped and if the temperature was

lower than 25 Celsius, the efficiency might have raised.

The relationship between the tilt angle and the short circuit current shows that these two

variables have a linear relationship or are directly proportional to each other. As for the relationship

between the tilt angle and the open circuit voltage, the relationship seems to be a polynomial based on

the data. However, in theory, the irradiance and voltage relationship is one where there is a steep

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increase in voltage as the irradiance rises while the change in voltage becomes smaller as the irradiance

gets larger until it reaches a maximum voltage. And since the irradiance is a direct relationship with the

tilt angle, the voltage and tilt angle relationship should be the same as the voltage and irradiance

relationship. This shows that there is error amongst our data. The error bars in Figures 6 and 7 are due

to the tilt angle where each measured tilt angle has a range of approximately +/- 5 degrees. During the

experiment, these tilt angles were calculated using the Pythagorean relationship of 90 degree triangles.

It may not be as accurate as using a protractor. If the angle changes, the irradiance changes as well.

With this said, Figures 29 and 30 show the relationship between maximum voltage and irradiance and

maximum power and irradiance, respectively. The data shows the same relationship described earlier

when the variables were compared to tilt angle. Basically, as the irradiance increases, the voltage

increases (while decreasing in the change in voltage) until it reaches a maximum irradiance that can be

absorbed. The power is the same except that the increase in power is steady. According to this data set,

at 50 degree (+/- 5 degree) tilt angle of the panel, the maximum power output occurs for the Kyocera

panel. The significance of this angle is that this is the angle at which the sunlight should be perpendicular

to the solar panel, hence, creating the maximum efficiency. This angle of maximum power production is

dependent upon the location on earth and the time of the day. If we changed location on earth and the

time of the day, it could change both the zenith angle and the azimuth angle. The location of the

maximum power point on the I-V curve is almost at the middle of the I-V curve line. The max current

approximately 7% away from the short circuit current and the max voltage is approximately 25% away

from the open circuit voltage.

Effect of Shading on PV Panel Performance

In vertical shading, it follows a pattern in which the voltage remains relatively constant while the

current drops. In the case of horizontal shading, the current drops when the shading starts then remains

rather constant as the voltage drops. As evidenced in Figures 10 and 11, the results were somewhat

16

inconsistent. For example as seen in Figure 10, in the case of 1 Cell Shaded and 3 Cells shaded, the curve

appears to be dented in where the Pmpp is in the baseline case of no shading.

As evidenced in Figure 12 and Figure 13, when plotting ratio of Pmpp of the shaded to the un-

shaded panel as a function of the ratio of total shaded area, the data from the horizontal shading had a

better linear regression fit. This is most likely due to the inconsistent irradiance during testing. Since it

was a scattered cloudy day and the wind was moving the clouds in and out of the sun, it caused the

irradiance to vary in between tests. When analyzing the irradiance between subsequent tests as shown

in Figure 31, it can clearly be seen that the irradiance spiked when taking the baseline measurement

00 01 02 03 04 05 06 07 08 09 10 11 120

500

1000

Irradiance vs Number of Cells Shaded

# Cells Shaded While Testing

Sola

r Ir

radi

ance

(Er)

[W/m

^2]

Figure 31. Plot of measured irradiance from the pyranometer when different measurements were taken.

with no shading, and taking the measurements when shading 7 and 11 cells vertically. Though the

horizontal shading better linear fit, it is likely due to the irradiance spikes present when taking the

vertical shading measurements. When omitting the vertically shaded measurements for 7 and 11 cells,

the linear regression would have a much better fit with an R2 value of 0.672.

When fitting a linear regression to the plot of the ratio of the shaded to un-shaded area as a

function of the panel efficiency, the horizontal panel shading has a better fit. This can once again can be

explained by the fact that the irradiance spiked. Since the horizontal fit is near-perfect and when

omitting the outlying irradiance measurements, the vertical regression still has a value of R2 = 0.7665, it

is an unlikely reason and the horizontal shading is presumed to fit the linear regression.

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Due to these results, when designing a PV system, it would be best to design for horizontal

shading since the efficiency followed a linear pattern vs. the ratio of shaded area. The horizontal shading

test follows the pattern exemplified by a circuit system wired in series, where the voltage adds up and

the current stays the same.

Effect of Temperature on PV Panel Performance

Plotting the data collected from both tests (Figures 18 and 19) performed during the

experiment, it was observed that the electrical conversion efficiency decreases linearly with the increase

of the panel temperature. This may be because at higher temperatures, the materials in the module

perform less efficiently. The electrical conversion is inversely proportional to the temperature of the

panel, therefore the higher the temperature of the solar panel, the smaller the efficiency. As expected,

the global horizontal irradiance (GHI) is directly proportional to the electrical conversion efficiency, the

efficiency decreases as the global horizontal irradiance values decreases.

The voltage- temperature coefficient for test #1 is about 15.3% smaller than the rated value

(-0.051 V/degC) and test #2 is about 16.8% smaller than the rated value. The experimental values from

test#1 and test #2 have a difference of 8.9% which shows that both tests were performed successfully,

but the measurements were taken at different times. The experimental voltage-coefficient is smaller

than the rated value, probably due to the temperature of the panel and solar angle. The current-

temperature coefficients for test #1 is about 29.1% smaller than the rated value (0.000626A/degC) and

for test #2 is about 55% smaller than the rated value. The significant difference between the coefficient

values from both tests #1 and #2 could be related to the amount of solar irradiation when the

measurements were taken. Solar irradiation decreases as the day continues.

On the other hand, when using the calculated GHI averages to calculate the Impp corrected, the

current-temperature coefficients for both tests #1 and #2 differed by 19.7% and 6.001% respectively.

The percentage difference between the experimental current-coefficient and the rated value decreased

18

by 32% for test#1 and 89.1% for test #2, which shows that linearizing Impp GHI coefficient gives a value a

lot closer to the actual value.

For both tests, the graph shows the dependency of the voltage with irradiance, the graphs

clearly show that the voltage values decreases linearly with smaller values of the GHI. On the other

hand, the current is linearly increased with the lower values of GHI. This trend can be observed on the I-

V curve where it shows that the voltage decreases with less irradiation whereas the current drastically

increases with higher irradiation.

The difference between the calculated averages of GHI for both tests was 2.34% which is

relatively small. This small difference of the GHI values is probably due to the difference of the time that

the measurements were taken at different temperatures of the solar panel.

The Impp between tests 1 and 2 was 3.97%. This difference between the currents values of test

1 and 2 was also probably due to the different times that the data was collected.

Plotting the calculated corrected electrical conversion efficiency as a function of temperature, it

was observed the slope for test#1 was smaller by 28.56% and slope for test #2 was smaller by 29.17%

than the non-corrected electrical efficiency conversion as function of the panel temperature. These

values show that the corrected efficiency value decreases slower by roughly 30% for both tests. This

significant difference between both graphs is due to the Impp averaged current values calculated from

both measurements that were used to calculate the corrected power and the efficiency.

VI. Conclusion

The photovoltaic modules performance is affected by the tilt angle, shading, and temperature.

When the direct solar radiation is perpendicular to the photovoltaic module, the performance is at its

maximum efficiency. With this said, the panel should be pointed toward south if standing north of the

equator. Also, depending on the time of the day, the position of the sun in the sky will change the zenith

19

and azimuth angles which mean that the solar module should follow this change throughout the day to

maximize the efficiency.

The direction of shading on a panel affects both its efficiency and the power collected by the

panel. Since the irradiance varied while conducting the experiment, the data is shown to be

inconclusive. However, it is very likely that horizontal shading has greater efficiency based on the results.

Therefore, when installing solar panels, one should consider installing the system in a way to minimize

shading in vertical direction.

The performance of the solar panel is maximized at a lower temperature compared to a higher

temperature. The range of temperature tested was from approximately 7o Celsius and 40o Celsius. The

measured data compared to the rated performance had errors that were less than 20%. To apply this,

one should not over-heat the solar panels in any way.

Based on this experiment, a south-facing solar panel in a cool environment with minimal vertical

shading (or any shading overall) would be optimal.

VII. References

Nottrott, Anders., "PV Panel Performance and Tilt", University of California at San Diego. Santa Monica, CA, Feb. 2012

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