# How Do Photovoltaic Cells Generate Electricity Engineering Essay

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## Introduction

The purpose of this experiment is to determine the extent to which the temperatures at which photovoltaic panels operate affect its performance in terms of voltage, current and power produced. Photovoltaic panels (or PV panels) are usually used to produce electricity in areas receiving long hours of sunlight and thus often experience elevated temperatures. This investigation of the impact of raised temperatures on the efficiency of PV panels can ultimately help determine whether or not a cooling system would be beneficial in the production of solar energy. This topic particularly interests me as I believe the renewable energy sector is rapidly developing and there is great room for further research and growth, especially with regards to the efficiency of solar energy.

'Temperature coefficient' is the derivative of a certain parameter (such as current) with respect to temperature. For my investigation, I will obtain the temperature coefficients for short-circuit current (Isc), maximum power current (Imp), open circuit voltage (Voc), and maximum power voltage (Vmp). The set-up for each of these is as follows:

Short circuit current (Isc) or maximum current is produced when there is no resistance and no voltage in the circuit and therefore there is a short circuit between the positive and negative terminals.

Open circuit voltage (Voc) is produced when there is a break in the circuit and hence under this condition, resistance is infinite and current is zero. [1]

Maximum power current (Imp) is the current that is obtained when the set-up is connected to a load and is operating at its peak performance parameters (maximum power, Pmp).

Maximum power voltage (Vmp) is the voltage that is obtained when the set-up is connected to a load and is operating at its peak performance parameters (maximum power, Pmp). [2]

I will find the maximum power output, Pmp, of the PV panels based on the collected range of data and plot the graphs of these parameters versus different operating temperatures in order to develop a relation between them. The power output (P) will be found using a variation of Ohm's law which states that current (I) is directly proportional to the voltage (V) across the circuit, and inversely proportional to the total resistance of the circuit (R), as seen in the following equation:

V = IR

P = VI

## Background

## How do photovoltaic cells generate electricity?

PV cells are made of semiconductors, such as the commonly-used silicon. When photons of light are incident on the photovoltaic cell, the absorbed photons free electrons from their atoms. "Holes" are created by the vacancies left by the escaped electrons. Due to the special structure of the PV cell, the freed electrons will move toward the holes when a conducting wire is connected across its terminals via the external circuit. As a result of this, a potential difference and current, flowing in the direction opposite to the electrons, is generated. This process, known as the photovoltaic effect, is shown in Fig 1 [3] .

## Fig 1: Photovoltaic Effect in PV cells

## Why are photovoltaic panels affected by temperature?

PV panels are composed of an array of interconnected, packaged PV cells. They are usually dark blue or black in color, and hence absorb heat quickly. Like most conductive materials, semiconductors experience a change in resistance with change in temperature. The change in resistance per degree Celsius of temperature change is called the temperature coefficient of resistance and is negative for semiconductors, indicating that the resistance of semiconductors decreases with increased temperatures. As a result, at higher temperatures, voltage decreases while current increases as V = IR. Since P = VI, depending on the extent to which each is affected the total power output could increase, decrease, or remain the same.

## What is a characteristic resistance (Rc)?

Characteristic resistance is the load in the external circuit for which power output is maximum (Vmp, Imp in Fig2). In order to obtain the characteristic resistance for a particular solar cell at a particular temperature, the current vs. voltage graph (I-V curve) has to be plotted while changing the resistance [4] . The point on the graph which has maximum area under it, gives the voltage and current at which maximum power is produced as shown in Fig2 [5] :

Fig 2: Obtaining Pmp, Vmp & Imp from an I-V curve

The character resistance is calculated as follows:

## Experimental Method

## Pre-Experiment Decisions

The first decision to be made is the type of solar cell or panel to be used for the experiment. A single solar cell typically produces a current of approximately 400mA and a voltage of 0.5V. As these are very small readings, the difference in the readings when the temperatures are changed will also be minute and hence it would be more practical to use a solar panel for my experiment instead. There were two solar panels of different power ratings (manufactured by Supreme Value Lighting, China) available to me: a 10-watt PV panel and a 20-watt PV panel. As the current and voltage generated by the 20-watt panel and the 10-watt panel would be too high for the current and voltage probes available to me, I chose to use the 2-watt panel to avoid any damage to the equipment. By reading the model specifications of the panel listed by the manufacturer, I made sure all the equipment had ratings higher than what those to be generated by the panel. I chose to use an amorphous silicon panel with the following specifications:

Testing Conditions

AM1.5, Ec=1000W/m2, Tc=25°C

Rated Maximum Power

2Wp

Maximum System Voltage

715V

Rated Voltage

8.73V

Rated Current

0.18A

Open Circuit Voltage

10.05V

Short Circuit Current

0.20A

The second important decision that I made was the method of obtaining the Vmp and the Imp for each temperature level. Since the Rc is different at each temperature, it would be very time consuming to plot the I-V curve and calculate the maximum area for each. For the sake of simplicity and ease of calculation, I chose to approximate the value of Rc to be as follows:

Fig 3: Approximation of Rc using I-V CurveThis approximation is illustrated on the graph in Fig 3 [6] :

Another important decision was choosing the best method of changing the temperature of the panel. After some research, I found it would be best to cool the panel in an air-conditioned room before starting the experiment and then placing it in the sun. If the panel is to be cooled below the room temperature, crushed ice placed in a Ziploc bag can be used. If the panel is to be heated above outdoor temperature, a heating pad can be placed at the back of the panel.

## Apparatus Used:

1 2W Solar Panel

1 Rheostat

1 Voltage Probe

1 Current Probe

2 Temperature Sensors

Black Insulating Tape

Connecting wires

Alligator clips

1 Vernier LabPro® Data Logger

1 Laptop (to connect data logger)

Crushed ice in a Ziploc bag

Heating Pads

Table (to place PV panel on)

## Procedure:

The solar must initially be kept indoors and cooled below room temperature by placing the Ziploc bag containing ice. While setting up the circuit, care must be taken to ensure that the positive terminal of the probe is connected to the positive terminal of the solar panel and the negative is connected to the negative. In addition, the leads should not be inserted into the panel while it is in direct sunlight as photovoltaic panels are live and may cause sparking. The temperature probe must be covered and attached to the surface of the panel using black insulating tape to ensure maximum absorption. The temperature probes should be attached in a constant position so that it does not affect the exposed surface area.

The temperature sensors and the current probe should be connected to the data logger and the set-up should be moved out under the sunlight. As the temperature is about to approach the outside temperature, the heating pad should be placed behind the cell in such a way that it does not come in direct contact with the temperature probes or obstruct the incident light in any way. Procedures should be repeated in order to minimize errors that could affect readings. The circuit diagram for each of the graphs is shown below:

Photovoltaic Panel

Current Probe

A

Temperature Sensor 2

Temperature Sensor 1

## +

_For graph of Isc vs. temperature (T) (Fig 4):

Fig 4: Schematic for obtaining graph of Isc vs. T

Photovoltaic Panel

Voltage Probe

V

Temperature Sensor 2

Temperature Sensor 1

## +

_For graph of Voc vs. temperature (T) (Fig 5):

Fig 5: Schematic for obtaining graph of Voc vs. T

Fig 6: Schematic for obtaining graphs of Vmp vs. T and Imp vs. T

## +

## _

Photovoltaic Panel

Voltage Probe

V

Temperature Sensor 2

Temperature Sensor 1

Ammeter

A

RheostatFor the graphs of Vmp vs. T and Imp vs. T(Fig6):

For every two degrees of temperature rise, the Rc should be calculated from the Voc and Isc data using the formula mentioned earlier and recorded in a table. (Rc=Voc/Isc).

As the temperature rises, the resistance on the rheostat should be adjusted to Rc for that temperature.

## Mathematical Model

On obtaining the graphs of Isc, Voc, Vmp, Imp vs. T, the linear temperature coefficients (Î±sc, Î²oc, Î²mp, Î±mp respectively) can be obtained by finding the derivatives of these parameters with respect to temperature. Thus, at a given temperature T, the parameter Q is given by:

Where,

Q is the performance parameter

T is the temperature at which property is measured

T0 is the reference temperature

âˆ†T is the difference between T and T0

Î± or Î² is the linear temperature coefficient

(Equation1)Therefore:

(Equation 2)

Since P = VI

(Equation 3)Ignoring the,

By replacing the values of V0, I0, Î±, Î² and T0 in equation 3, a relation between T and Pmp can be obtained which is to be graphed. The temperature coefficient of Pmp may then be obtained by finding the derivative of Pmp with respect to T.

## Data Collection

## 4.1. Raw data for Open Circuit Voltage vs. Temperature

## Temperature (°C + 0.1)

## Open Circuit Voltage (Voc) (V ± 0.0300)*

## Trial 1

## Trial 2

## Trial 3

## Average

25.0

10.0300

10.0211

10.0251

10.0254

26.0

9.9873

9.9418

9.9687

9.9659

27.0

9.8874

9.8852

9.8859

9.8862

28.0

9.8322

9.7975

9.8080

9.8126

29.0

9.7140

9.7030

9.7042

9.7071

30.0

9.6115

9.6317

9.6653

9.6362

31.0

9.5605

9.5584

9.5592

9.5594

32.0

9.4999

9.5108

9.4893

9.5000

33.0

9.4055

9.4032

9.4031

9.4039

34.0

9.3412

9.3300

9.3308

9.3340

35.0

9.2466

9.2513

9.2521

9.2500

*Note that although the accuracy of the voltage probe was up to ±0.0001V, the error was taken as ±0.03 due to constant fluctuations in the readings. The error was calculated by finding the maximum deviation of a reading from its mean. This represents the random uncertainty of the experiment.

## Temperature (°C + 0.1)

## Short Circuit Current (Isc) (A ± 0.0050)*

## Trial 1

## Trial 2

## Trial 3

## Average

## 25.0

## 0.1859

## 0.1845

## 0.1842

## 0.1849

## 26.0

## 0.1891

## 0.1891

## 0.1895

## 0.1892

## 27.0

## 0.1925

## 0.1925

## 0.1927

## 0.1926

## 28.0

## 0.1985

## 0.1970

## 0.1966

## 0.1974

## 29.0

## 0.2050

## 0.2072

## 0.2036

## 0.2053

## 30.0

## 0.2126

## 0.2122

## 0.2113

## 0.2120

## 31.0

## 0.2134

## 0.2140

## 0.2207

## 0.2160

## 32.0

## 0.2244

## 0.2238

## 0.2215

## 0.2232

## 33.0

## 0.2275

## 0.2303

## 0.2286

## 0.2288

## 34.0

## 0.2341

## 0.2368

## 0.2362

## 0.2357

## 35.0

## 0.2448

## 0.2449

## 0.2446

## 0.24484.2. Raw data for Short Circuit Current vs. Temperature

*Note that although the accuracy of the current probe was up to ±0.0001A, the error was taken as ±0.005A due to constant fluctuations in the readings. The error was calculated by finding the maximum deviation of a reading from its mean. This represents the random uncertainty of the experiment.

## 4.3. Obtaining Characteristic Resistance

## Temperature (°C + 0.1)

## Short Circuit Current (Isc) (A ± 0.0050)

## Open Circuit Voltage (Voc) (V ± 0.0300)

## Characteristic Resistance (Rc) (Î© ± 1)*

25.0

0.1849

10.0254

54

26.0

0.1892

9.9659

53

27.0

0.1926

9.8862

51

28.0

0.1974

9.8126

50

29.0

0.2053

9.7071

47

30.0

0.2120

9.6362

45

31.0

0.2160

9.5594

44

32.0

0.2232

9.5000

43

33.0

0.2288

9.4039

41

34.0

0.2357

9.3340

40

35.0

0.2448

9.2500

38

*Note that although the error should be 3% considering the accuracy of the voltage and current probes, the error is taken as ±1Î© as that is the accuracy of the rheostat used

In the above table, the characteristic resistance for each temperature was obtained by dividing the open circuit voltage by the short circuit current.

## 4.4. Raw data for Maximum Power Voltage vs. Temperature and Maximum Power Current vs. Temperature

## (On next page)

## Temperature (°C + 0.1)

## Trial 1

## Trial 2

## Trial 3

## Average

## Characteristic Resistance (Rc) (Î© ± 1)

## Maximum Power Voltage (Vmp) (V±0.0700)*

## Maximum Power Current (Imp) (A ± 0.0020)*

## Maximum Power Voltage (Vmp) (V±0.0700)*

## Maximum Power Current (Imp) (A±0.0020)*

## Maximum Power Voltage (Vmp) (V±0.0700)*

## Maximum Power Current (Imp) (A±0.0020)*

## Maximum Power Voltage (Vmp) (V±0.0700)*

## Maximum Power Current (Imp) (A±0.0002)*

25

54

8.7601

0.1622

8.7163

0.1628

8.7139

0.1631

8.7301

0.1627

26

53

8.6512

0.1659

8.6479

0.1666

8.6470

0.1664

8.6487

0.1663

27

51

8.6194

0.1673

8.5897

0.1681

8.5888

0.1683

8.5993

0.1679

28

50

8.4826

0.1732

8.4738

0.1725

8.4674

0.1730

8.4746

0.1729

29

47

8.3941

0.1784

8.3972

0.1779

8.3700

0.1789

8.3871

0.1784

30

45

8.3039

0.1821

8.3178

0.1816

8.2945

0.1811

8.3054

0.1816

31

44

8.2587

0.1866

8.2223

0.1861

8.2480

0.1874

8.2430

0.1867

32

43

8.1331

0.1939

8.1354

0.1929

8.1251

0.1940

8.1312

0.1936

33

41

8.0789

0.1964

8.0551

0.1973

8.0667

0.1967

8.0669

0.1968

34

40

8.0013

0.2069

7.9878

0.2057

7.9884

0.2031

7.9925

0.2052

35

38

7.9842

0.2101

7.8241

0.2103

7.8713

0.2091

7.8932

0.2098

*Note that although the accuracy of the current and voltage probes were up to ±0.0001A and ±0.0001V, the error for the maximum power current was taken as ±0.002A and the error for the maximum power voltage was taken as ±0.07V due to constant fluctuations in the readings. The errors were calculated by finding the maximum deviation of readings from their means. This represents the random uncertainty of the experiment.

Î’mp = -0.084

Î²oc = -0.0784

Î±sc = 0.0006

Î±mp = 0.0048

## Data Analysis

From the above data and graphs of the data, it can be concluded that current and voltage produced by a solar panel are both linearly related to the temperature at which the panel is operating. The voltage has a negative slope while the current has a positive one against temperature which implies that an increase in temperature results in an increase in the current produced and a decrease in the voltage produced by a greater proportion(slope of voltage graph has a greater numerical value). In the case of the solar panel used above, the linear temperature coefficient of the maximum power voltage was found to be -0.084 (slope of the graph) and the linear temperature coefficient of the maximum power current was found to be 0.0048 (slope of the graph). Using the mathematical model illustrated earlier, the maximum power at each temperature can be obtained using the formula:

The table shown below states the maximum power output at each temperature:

## Temperature (°C + 0.1)

## Maximum Power (Pmp) (W ± 3%)

25.0

2.105532

26.0

1.986078

27.0

1.866623

28.0

1.747169

29.0

1.627715

30.0

1.508261

31.0

1.388806

32.0

1.269352

33.0

1.149898

34.0

1.030444

35.0

0.910989

The following data was then graphed as follows:

## Conclusion

It can be seen from the above graph, that the power decreases linearly with temperature and has a linear temperature coefficient of -0.1195 which is the gradient of the graph. The graph would cut the temperature axis at 42.61°C. This indicates that at this temperature, the power output would be zero. The experiment would have to be carried out at higher temperatures in order to determine whether or not this stands true.

Thus, by examining all the graphs, the extent to which the temperature at which a solar cell operates affects the voltage, current and power produced can be determined. They are all affected linearly and the rate at which each is affected can be determined by the slope of the graphs which are all shown in the form y = mx + c where m is the slope. It can be seen that solar panels tend to produce a higher power output at lower temperatures. This is because voltage decreases at a greater rate with reference to temperature than the rate of increase in current with reference to temperature. After looking up some online sources, I obtained a table of temperature coefficients of voltage and current for different solar modules.

## Module

## dIsc/dT

## dImp/dT

## dVoc/dT

## dVmp/dT

ASE300, mc-Si .

0.00091

0.00037

-0.0036

-0.0047

AP8225, Si-Film

0.00084

0.00026

-0.0046

-0.0057

M55, c-Si

0.00032

-0.00031

-0.0041

-0.0053

SP75, c-Si

0.00022

-0.00057

-0.0039

-0.0049

MSX64, mc-Si

0.00063

0.00013

-0.0042

-0.0052

SQ-90, c-Si

0.00016

-0.00052

-0.0038

-0.0048

MST56, a-Si

0.00099

0.0023

-0.0041

-0.0039

UPM880, a-Si

0.00082

0.0018

-0.0038

-0.0037

US32, a-Si

0.00076

0.0010

-0.0043

-0.0040

SCI50, CdTe

0.00019

-0.0012

-0.0037

-0.0044

From the above table, it can be seen that most solar modules have temperature coefficients of voltage whose absolute values are greater than those of the temperature coefficients of current. This implies that the temperature coefficient of power will be negative as the temperature coefficient of voltage is negative. Thus it can be concluded that in most cases the power output of the module decreases with increase in cell temperature.

However, the effectiveness of a cooling system in order to maximize power output cannot be determined without knowing how much power it would take to run the cooling system itself. Generally, cooling systems require a lot of power which may be greater than the extra power produced by cooling the panels down and thereby yielding no real benefit.

## Evaluation

There were several errors that affected this experiment. A possible error could be caused by the fact that the intensity of the incoming light from the sun may not have always been the same while the trials were taken. This could prove problematic as the amount of power generated is dependent on the light intensity. The tilt of the panel and thereby the angle at which light strikes the solar panel could have changed while the experiment was modified to measure different parameters. The tilt affects the power generated by means of a cosine function. Also, the temperature readings of the temperature sensor could have also been affected if they came in contact with the heating pad or icepack. There was also an error caused on account of the rheostat as it was hard to change the resistance while the temperature rose. In addition, the black insulating tape used to attach the temperature sensors to the surface of the panel covered some portion of the panel and thus reduced its power output. This reduction of exposed surface area may not have been constant as the experiment was conducted over several days. Despite the errors of this experiment, it helped prove that the power output and therefore the efficiency of a solar panel is reduced at higher temperatures and thus large systems may lose out on a lot of power that could be generated if temperatures are too high.

## Unresolved Questions

Will the linear relation hold true at temperatures higher and lower than those studied in this essay?

Will a cooling system actually help increase power output or will it consume more power than it will help produce?