Solar Cells

A solar cell is a semiconductor device that convert solar energy into electrical energy directly without going through any immediate energy conversion steps. It is a fundamental block of solar photovoltaic (PV) technology. Many solar cells are connected together to form solar PV modules. Several solar PV modules are connected together to make PV array in small power applications as well as in big power plant applications. Therefore, it is important to understand how does a solar cell work, how to identify a solar cells, what are its parameters, how much power a solar cell can generate, how the generated power depends on sunlight falling on it etc. This chapter focuses on providing the fundamental understanding of solar cells, its parameters and how the variation in parameter and ambient conditions affect the performance of solar cells of different technologies.

3.1   How Solar Cells are better than any conventional source of electricity ?

The Electricity is conventionally generated by using coal energy, hydro energy or nuclear energy. One of the most common ways of generating electricity is using coal energy. In India about 55% of electricity is generated using coal energy . A typical coal power plant, shown in figure 3.1, involves several steps before the energy of coal gets converted into useful energy form, the electricity. The power plant process starts from the burning of coal and ends with the generation of electricity by generators. In the whole process, only fraction of coal energy is wasted in the conversion process and transmission of electricity from power plant to our homes. Other than the waste of energy, there is also environmental pollution caused of coal based power plants. Also, coal as a source of energy is not available in infinite quality, which means that sooner or later we will run in the shortage of coal. Considering these facts, one must look for alternate source of energy.

One of the modern ways of generating electricity is using solar cells or solar Photovoltaic (PY); a technology that converts sunlight into electricity. Solar cell and its technology have drawn lots of attention of engineers, researchers, industries and governments in recent times. Therefore, in this chapter, we will focus on solar cells. So, let us see what is a solar cell ? How is current generated by it and what are its applications ? 

3.2   What is a Solar Cell ?

Solar cell is a semiconductor device which directly converts sunlight into electricity. Solar cell converts sunlight into electricity by photovoltaic effect. Hence, they are also called photovoltaic cell. A typical commercial silicon solar cell is shown in figure 3.2.

A solar cell generates current and voltage at its terminals when sunlight falls on it. The amount of electricity generated by a solar cell depends on the amount of sunlight incident on it. The electricity generated by solar cell depends upon the intensity (amount) of light, the area of a cell and the angle at which light falls on it. The higher is the intensity of sunlight, the more is the electricity generated by solar cell. If area of a solar cell is increased, the current generated by it increases. The power generated by the solar cell is optimum when sunlight falling is perpendicular to the front side of solar cell.

In common, all solar cells, irrespective of the technology and material used have only two terminals (positive and negative terminal) as output. Typically solar cells have front contact at the top, emitter-base junction or p-n junction in the middle and the back contact at the bottom. At the emitter- base junction, the separation of negative and positive charge take place. Electricity is supplied to a load by connecting its terminals to the front and back contacts of a solar cell or solar module or solar panel as shown in figure 3.3

3.3   How Solar Cell generates electricity ?

The sunlight falling on the earth is basically the bundles of photons or bundles of small energy. Each photon in a bundle has a finite amount of energy. In solar spectrum, there are many photons of different energy. For generation of electricity, photon must be absorbed by solar cell. The absorption of photon depends upon the energy of photon and the band- gap energy of semiconductor material of a solar cell. The photon energy and the band-gap energy of semiconductor is expressed in terms of Electron-volt (eV). The eV is a unit of energy.

So, the working of a solar cell can be explained as follows  : 

1. Photons in the sunlight falling on the solar cell’s front face absorbed by semiconducting materials.
2. Free electron hole pairs are generated. Electrons are considered as negative charge and holes are considered as positive charge. When solar cell is connected to a load, electron and holes near the junction are separated from each other. The holes are collected at positive terminal (anode) and electrons are negative terminal (cathode). Electric potential is built at the terminals due to the separation of negative and positive charges. Due to the difference between the electric potentials at the terminals we get voltage across the terminals.
3. Voltage developed at the terminals of a solar cell is caused to drive the current in the circuit. The current in the circuit will be direct current or DC current.

So, the solar cell with day light falling on it can directly drive DC electrical appliances. But, the amount of electricity generated is proportional to the amount of light falling. So, the amount of electricity generated through out the day  is not constant. The current generated also depends on several other parameters. In the following section we will now see why the generated current is not constant.

3.4Parameters of  Solar Cells.

A solar cell converts the sunlight into electricity. How nicely a solar cell does the conversion of sunlight into electricity is determined the parameters of solar cells. There are several parameters of solar cells that determine the effectiveness of sunlight to electricity conversion. The list of solar cell parameters is following :

• Short circuit current  (ISC)

• Open circuit voltage and (VOC )

• Maximum power point

• Current at maximum power point (I m)

• Voltage at maximum power point (V m)

• Fill factor (FF)
• Efficiency (n),

These parameters can be best understood by Current-voltage curve (I-V curve) of a solar cell. The representation of I-V curve is plotted in figure 3.4. The Y-axis is normally plotted as current axis and X-axis is plotted as voltage axis.

Using figure 3.4, the cell parameters are defined here. Normally the value of the cell parameters are given by a manufacturer or scientist at standard test conditions. (STC) which is corresponding to  1000 W/m2 of input solar radiation and 25°C cell operating temperature.

• Short circuit current (ISC): It is the maximum current a solar cell can produce. The higher the ISC better is the cell. It is measured in Ampere (A) or milli-ampere (mA). The value of maximum current depends on cell technology, cell area, amount of solar radiation falling on cell, angle of cell, etc. many times, people are given current density rather than current. The current density is obtained by dividing  ISC  by the area of solar cell (A).The current density is normally referred by symbol, ‘J’, therefore, the short circuit current density, Jsc is given by ISC/A.
• Open circuit voltage (Voc): It is the maximum voltage that a solar cell produce. The higher the Voc, the better is the cell. It is measured in volts(V) or sometimes milli-volts (mV). The value of this maximum open circuit voltage mainly depends on cell technology and operating temperature.
• Maximum power point (Pm or Pmax): It is the maximum power that a solar cell produces under STC. The higher the Pm  the better is the cell. It is given in terms of watt (W). Since it is maximum power or peak power, it is sometimes also referred as Wpeak or Wp. A solar cell can operate at many current and voltage combinations. But a solar cell will produce maximum power only when operating at certain current and voltage. This maximum power point is denoted in figure 3.4 as Pm. Normally, the maximum power point for a I-V curve of solar cells occurs at the ‘knee’ or ‘bend’ of the curve. In terms of expression Pm is given as : 

Pm or Pmax  = Im X  Vm

• Current at maximum power point (Im) : This is the current which solar cell will produce when operating at maximum power point. The Im will always be lower than ISC. It is given in terms of ampere (A) or milli-ampere (mA).
• Voltage at maximum power point (Vm) : This is the voltage which solar cell will produce when operating at maximum power point. The Vm will always be lower than Voc. It is given in terms of volt (V) or milli-volt (mV).
• Fill factor (FF) : As the name suggest, FF is the ratio of the areas covered by  Im –  Vm rectangle with the area covered by ISC – Voc Rectangle (both shown by dotted line in Figure 3.4), whose equation is given below. It indicates the square-ness of I-V curve. The higher the FF , the better is the cell. The FF of a cell is given in terms of percentage (%). Cell with squarer I-V curve is a better cell. 

 

Here the expression for  Pm or Pmax  can alternatively be written in terms of ISC , Voc  and FF as : 

Pm = ISC  X  Voc  X FF

• Efficiency  (ɳ) : The efficiency of a solar cell is defined as the maximum output power (Pm or Pmax) divided by the input power (Pin).  The efficiency of a cell is given in terms of percentage (%), which means that this percentage of radiation input power is converted into electrical power.  Pin for STC is considered as 1000 W/m2. This input power is power density (power divided by area), therefore, in order to calculate the efficiency using Pin at STC, we must multiply by solar cell area. Thus, efficiency can be written as :

Let us now see what the possible values of solar cell parameters and how the values that depend on the various solar cell technologies.

 Worksheet 3.1 :  Fill below in Table 3.1, the various solar cell parameters and their units by which they are presented.

TABLE 3.1 Solar Cell Parameters and their units

S. No.	Name of Parameter	Unit of Parameter
1
2
3
4
5
6
7

 

Example 3.1 The current density of a solar cell having an area of 100cm2 at Standard Test Condition (STC) is given as 35mA/cm2. Find out the output current of solar cell.

 Solution First, we write the formula for current density of a solar cell given by where,

Jsc = Current density (mA/cm2)

Isc = Output current (mA)

A= Area (cm2)

Given that, Jsc = mA/cm2

So, the expression for solar cell current can be written as:

Output current (Isc) = Jsc X A (mA)

Now, given that area for solar cell is 100 cm2, then 

Output current (Isc) = 35 mA/cm2 X 100 cm2 = 3500 mA or 3.5A

Similarly, we calculate output current for different values of solar cell area in the Table 3.9

Example 3.2 A solar cell gives a current of 0.6 A and voltage of 0.5V at maximum power point. What is the maximum power point of the solar cell ? 

Solution First, we write the formula for the maximum power point of a solar cell, given by

Pm or Pmax  = Im X Vm

Given that, Im = 0.6A

Vm = 0.5V

Therefore, the maximum power point, Pm = 0.6A X 0.5V = 0.3W.

Example 3.3 A solar cell having an area of 100cm2 gives 3.1 A current at maximum power point and 0.5 V at maximum power point at STC. The cell gives 3.5A short current and 0.6V open circuit voltage. What is the maximum power point of the solar cell? Also find out the efficiency of the cell.

  Solution First, we write the formula for the maximum power point of a solar cell, given by

Pm or Pmax  = Im X Vm

Given that,

Isc = 3.5 A

Im = 3.1 A

Voc = 0.6 V

Vm = 0.5 V

Maximum power point, Pm =3.1 A X 0.5 V = 1.55 W

Now , we write the formula for efficiency of a solar cell given by

 

Where,

ɳ =  Efficiency in percent (%)

Pmax = Output power in watt (W)

Pin = Light input power per unit area in watt/sqr meter (W/m2)

A = Solar cell area in square meter(m2)

ɳ = ?

                                               We know, Pm = 1.55 W and  at STC, Pin = 1000 W/m2

First, we convert the unit of area from square centimeter (cm2) to square meter (m2) by dividing area in cm2 by 10000

Here,  A=100 cm2 = 100 x 10-4  m2 = 0.01 m2

Now, putting the number we can calculate the efficiency of the cell.

Thus efficiency of the solar cell is 15.5%.

Example 3.4 Refer the characteristic curve (Figure 3.5) and find out the Fill Factor for the   solar cell.

Solution Short circuit current (Isc) = 0.45 A

Open circuit voltage (Voc) = 0.7 V

Current  at maximum power point (Im) =0.40 A

Voltage  at maximum power point (Vm) =0.5 V

Now, 

Maximum power point, Pm or Pmax   = Im X Vm = 0.40 X 0.5= 0.2 W

Note : In order to represent the FF value in ‘percentage’, multiply by 100.

Example 3.5 A solar cell having an area of 25 cm2 gives a current of 0.85 A and voltage is 055 V at maximum power point. The short circuit current is 0.9 A and open circuit voltage is 0.65 V. What is the Fill Factor, maximum power point and efficiency of the solar cell ? Consider STC.

Solution Given, Short circuit current (Isc) = 0.9 A

Open circuit voltage (Voc) = 0.65 V

Current  at maximum power point (Im) =0.85 A

Voltage  at maximum power point (Vm) =0.55 V

Light input power (W/m2) = 1000 W/m2

Area = A=25 cm2 = 25 x 10-4  m2 = 0.0025 m2

Now,

Maximum power point, Pm or Pmax   = Im X Vm = 0.85 X 0.55= 0.4675 W

Note : In order to represent the FF and efficiency values in ‘percentage’, multiply by 100 in both cases.)

Example 3.6 A solar cell having Fill Factor (FF) 60% gives 2.5A current at maximum power point at STC. The cell gives 3 A short circuit current and 0.5 V open circuit voltage.

Solution Given that,

Isc = 3 A

Im = 2.5 A

Voc = 0.5 V

Vm = ?

FF = 60%

First, we write formula for Fill Factor of a solar cell given by

Where,

Isc = Short circuit current (A)

Im =  Current at maximum power point (A)

Voc = Open circuit voltage (V)

Vm = Voltage at maximum power point (V)

FF = Fill Factor (%)

We know, FF = 60%

First, we convert Fill Factor (FF) from percent to decimal by dividing it by 100.

Therefore,

Now, we rewrite the formula for Fill factor of a solar cell to get the value of Vm given by expression below.

Voltage at maximum power point, Vm = FF 

Now, putting the value, we can calculate the voltage at maximum power point.

Thus the voltage at maximum power point is 0.36V.

Example 3.7 A solar cell having Fill factor (FF) 68% gives 0.6 V voltage at maximum power point at STC. The cell gives 3 A short circuit current and 0.7 V open circuit voltage. What is the current at maximum power point of the solar cell ? 

Solution Given that,

Isc = 3 A

Im = ?

Voc = 0.7 V

Vm = 0.6 V

FF = 68%

First, we write formula for Fill Factor of a solar cell given by expression below

Where,

Isc = Short circuit current (A)

Im =  Current at maximum power point (A)

Voc = Open circuit voltage (V)

Vm = Voltage at maximum power point (V)

FF = Fill Factor (%)

We know, FF = 60%

First, we convert Fill Factor (FF) from percent to decimal by dividing it by 100.

Now, we rewrite the formula for Fill factor of a solar cell to get the value of Im given by expression below.

Now, putting the value, we can calculate the current at maximum power point.

Thus, current at maximum power point is 2.38 A.

Example 3.8 A solar cell has maximum power point of 0.3 W. The cell voltage at maximum power point at STC is 0.65 V. What is the current at maximum power point of the solar cell ? 

Solution Given that,

Pm = 0.3 W

Im = ?

Vm = 0.65 V

First we write the formula for Maximum power point, Pm or Pmax   of a solar cell given by 

Maximum power point, (Pm )  = Im X Vm 

Where,

Pm = Maximum power point (W)

Im = Current at maximum power point (A)

Vm = Open circuit voltage (V)

Now, we rewrite the formula for maximum power point Pm of a solar cell to get the value of Im given by expression below.

Putting the value, we can calculate the current at maximum power point.

Thus, the current at maximum power point is 0.46 A.

Worksheet 3.2 Current and voltage of a solar cell has been measured under STC at various points of cell operation. These values are given in table 3.2 below. For this solar cell, calculate the maximum power that can be extracted from solar cell.

TABLE 3.2 Current and Voltage of a Solar Cell Under STC at Different Points of Operation

S.No.	Current I (A)	Voltage, V (V)	Power, P(W) = I x V
1	0.00	0.58
2	0.01	0.58
3	0.39	0.57
4	0.79	0.57
5	1.19	0.56
6	1.58	0.55
7	1.99	0.54
8	2.39	0.53
9	2.79	0.52
10	3.19	0.51
11	3.58	0.46
12	4.33	0.00

 

Worksheet 3.3 :  A Solar Cell’s current and voltage at various operating has been given in worksheet 3.2 Using that I-V data, fill in estimate and fill in the parameters of solar cell given in Table 3.3 below.

TABLE 3.3 Problem to find various  Solar Cell parameters based on Table 3.2

S.No	Parameters	Reading or calculating from Table 3.2	Values
1	Short circuit current (Isc)	Current value when voltage is zero
2	Open circuit voltage (Voc)	Voltage value when current is zero
3	Maximum power point, Pm	Value of maximum power
4	Current at maximum power point (Im)	Current value at maximum power point
5	Voltage at maximum power point (Vm)	Voltage value at maximum power point
6	Fill Factor (FF)
7	Efficiency

 

Worksheet 3.4 :  I-V characteristic of a solar cell is given below (Table 3.4). Fill in the blank spaces.

TABLE 3.4 Obtain the missing quantities

S.No.	Current I (A)	Voltage, V (V)	Power, P(W)
1	0.00	0.58	–
2	0.01	0.58	–
3	0.39	–	0.22
4	0.79	0.57	–
5	1.19	0.56	–
6	–	0.55	0.88
7	1.99	0.54	–
8	2.39	0.53	–
9	2.79	–	1.47
10	3.19	0.51	–
11	–	0.46	1.65
12	4.33	–	–

 

3.5   Solar Cell Technologies.

In market, a wide variety of solar cells are available. These cells are made of using different materials. The name of a particular solar cell or solar cell technology depends on the name the material used in that particular technology. The properties of materials used in different types of solar cells are different. Hence, different types of solar cells have different values of solar cell parameters like efficiency (ɳ), short circuit current density (Jsc), open circuit voltage (Voc) and fill factor (FF). The list of commercial solar cells technology, materials and efficiency is given in Table 3.5. The commonly available commercial solar cells along with (ɳ), A, (Jsc), (Voc) and (FF) are mentioned in Table 3.6.

TABLE 3.5 Commercial  Solar Cells Technology, Material and Efficiency

Solar photovoltaic technologies	Solar cell type	Material used	Efficiency (ɳ in percent)
Crystalline Silicon (c-si) solar cell	Mono-crystalline silicon  Poly or multicrystalline (Si (mc-Si)	Mono-crystalline silicon  multi-crystalline silicon	14-16                   14-16
Thin film solar cell	Amorphous Si (a-Si)       Cadmium telluride (CdTe)       Copper-Indium-Gallium-Selenide (CIGS)	Amorphous silicon        cadmium and tellurium      copper, Indium, Gallium,Selenium	6-9                             8-11                       8-11
Multi-junction solar cell	GainP/GaAs/Ge Gallium Indium phosphide/Gallium arsenide/Germanium	Gallium (Ga), Arsenic (Ar), Indium (In),Phosphorus (P), Germanium (Ge)	30-35

 

There are many commercially available solar cell technologies. The name of technology comes from the materials used in making solar cells. 

TABLE 3.5 Typical solar cell parameters (ɳ, Jsc, Voc and FF ) of Commercial Solar Cells with Available Cell Areas

Solar cell type	Efficiency (ɳ in %)	Cell area (A) (in cm2)	Output Voltage(Voc) (in V)	Output current(Jsc) (in mA/cm2)	Fill Factor(FF) (in %)
Mono-crystalline silicon	14-17	5-156	0.55-0.68 V	30-38	70-78
Poly or multicrystalline Si (mc-Si)	14-16	5-156	0.55-0.65 V	30-35	70-76
Amorphous Si (a-Si)	6-9	5-200	0.70-1.1 V	8-15	60-70
Cadmium telluride (CdTe)	8-11	5-200	0.80-1.0 V	15-25	60-70
Copper-Indium-Gallium-Selenide (CIGS)	8-11	5-200	0.50-0.7 V	20-30	60-70
Gallium Indium phosphide /Gallium arsenide/Germanium (GainP/GaAs/Ge)	30-35	1-4	1.0-2.5 V	15-35	70-85

 

The efficiency of solar cell  varies from one technology to other technology and from one manufacturer to other manufacturer.

3.6   Factor Affecting Electricity Generated by a Solar Cell.

There are five common factors that affect the power generated by solar cells. They are as follows : 

1. The conversion efficiency (ɳ)
2. The amount of light (Pin)
3. The solar cell area (A)
4. The angle at which day light falls  (Ɵ),and 
5. The operating temperature (T)

3.6.1   Effect of Conversion Efficiency ( ɳ)

Of the total light energy falling on a solar cell, only some fraction of the light energy gets converted into electrical energy by the solar cells. The ratio of electrical energy generated to the input light energy is referred as conversion efficiency of solar cells. The conversion efficiency of solar cell is fixed, based on material and the manufacturing process. Once a solar cell of given material is manufactured, its efficiency value becomes fixed and it cannot be changed.

Efficiency of a solar cell is given in terms of maximum power that solar cell can generate for a given input solar radiation. The maximum power output (Pmax  or Pout) of solar cells depends on voltage developed across cell terminal and current it can supply. The cell area also affects the power output. If the instantaneous solar radiation or power density is Pin, the expression for the efficiency (ɳ) of solar cell can be given as :

For given input power, the value of the output power is directly determined by the value of solar cell’s conversion efficiency and solar cell area. The solar cells with higher efficiency values will always give better performance. The unit of solar cell efficiency is percentage (%), the unit of Pout is normally watt, the unit of Pin is normally W/m2 and unit of cell area is in m2 or cm2. The solar cell efficiency is given for standard test condition (STC) and under the STC, the value of input power density, Pin is taken as 1000 W/m2 or 0.1 W/m2.  

Example 3.9 Calculate the output power from a solar if its efficiency (in %) is 30, 24, 19,16 and 12, input power density is 1000 W/m2, and area of the solar cell is 100 cm2.

Solution First, we write formula for Fill Factor of a solar cell given by

Where,

ɳ =  Efficiency in percent (%)

Pmax or Pout  = Output power in watt (W)

Pin = Light input power per unit area in watt/meter2 (W/m2)

A = Solar cell area in square meter2(m2)

ɳ =  30%, 24%, 19%, 16%, 12%

Pin = 1000 W/m2

Pmax = ?

First, we convert cell area from cm2 to m2 .

It is given that cell area A =100 cm2 = 100 X 10-4m2.

Now, we solve for solar cell of efficiency  30%

Above equation can be written as :

Pmax  = ɳ  X Pin X  A

We put the respective terms value and we get ,

Similarly, we calculate output power for other efficiencies in the table form as shown in Table 3.7.

TABLE 3.7 Table for Example 3.9

ɳ (%)	Pin (W/m2)	A (cm2)	A (m2)	ɳ/100	Pmax = (ɳ/100) X Pin X A (W)
30	1000	100	0.01	0.30	3
24	1000	100	0.01	0.24	2.4
19	1000	100	0.01	0.19	1.9
16	1000	100	0.01	0.16	1.6
12	1000	100	0.01	0.12	1.2

 

From the above table , it clear that when efficiency of a solar cell reduces the output power generated is also reduces. The output power of solar cell directly depends on the efficiency of solar cell as shown in Figure 3.6.

 

3.6.2 Change in the Amount of Input Light (Pin)  

We should keep in mind that the amount of sunlight (intensity of sunlight) falling on solar cells keeps changing from morning to evening. The current and voltage output of a solar cell depends on the amount of light falling on it. The electric current generated by solar cell is directly proportional to the amount of light falling on it. Suppose, a solar cell produce 1 A current under 1000 W/m2 input solar radiation, then under 500 W/m2 input solar radiation, the  cell will only produce  1/2  A current (because input radiation is half). As the amount of sunlight falling on the solar cell increases from morning till afternoon, the current output of a solar cell also increases from morning till afternoon. From afternoon, till evening, the amount of sunlight falling on the solar cell decreases, and hence, the current output of a solar cell also decreases from afternoon till evening. The output voltage of a solar cell is not affected strongly by change in the amount of light. If a solar cell produces 1 V at noon time, its voltage will roughly remain same in the morning as well as in evening hours.

The solar cell current output is proportional to the amount of solar radiation and voltage is relatively not affected by the variation in sunlight intensity. Therefore, the amount of power generated (Current X Voltage) by solar cell is proportional to the amount of light falling on it. The amount of power generated by the solar cells throughout the day keeps changing (i.e., it is not constant). So, a solar cell gives high power when the intensity of light falling is high. Similarly, less power is generated when the intensity of light falling is low.

   Example 3.10 Calculate the output power for solar cells of efficiencies 16 %. When the input power is say, 1000, 800, 600 and 400 W/m2, and area of the solar cell is 100 cm2.

Solution First, we write formula for efficiency of a solar cell given by

Where,

ɳ =  Efficiency in percent (%)

Pmax  = Output power in watt (W)

Pin = Light input power per unit area in watt/meter2 (W/m2)

A = Solar cell area in square meter (m2)

ɳ =  16%

Pin = 1000, 800, 400 W/m2

Pmax = ?

It is given that cell efficiency is 16% and cell area is A = 100 cm2

First, we convert area unit  from square meter (cm2) to meter (m2) by   dividing area in cm2 by  10000.

A =100 cm2 = 100 X 10-4m2 

Now, we solve for light input power  = 1000 W/m2

Above equation can be written as :

Pmax  = ɳ  X Pin X  A

We put the respective terms values and we get,

Similarly, we calculate output power for other efficiencies in table form as shown in Table 3.8.

TABLE 3.8 Table for Example 3.10

ɳ (%)	Pin (W/m2)	A (cm2)	A (m2)	ɳ/100	Pmax = (ɳ/100) X Pin X A (W)
16	1000	100	0.01	0.16	1.60
16	800	100	0.01	0.16	1.28
16	400	100	0.01	0.16	0.96
16	600	100	0.01	0.16	0.64

 

The amount of power generated by solar cell depends on the amount of light falling on a solar cell is shown in Figure 3.7. From above table, it clear that when amount of light falling on a solar cell reduces, the output power generated also reduces.

3.6.3 Change in Solar cell area (A)

The amount of maximum output current (Isc or short circuit current) of a solar cells depends on the area of a solar cells. The current output is directly proportional to the cell area. So, when solar cell area is large, the amount of electric current generated by it will be large. Similarly, less amount of electric current generated when the cell area is small. For a given amount of input sunlight if 100 cm2 cell produces 2 A current, then a 200 cm2 cell will produce  4 A current, and a 50 cm2 cell will produce 1 A current under same input sunlight intensity. When we divide the generated current by area of solar cells, we get current / area or current per unit area, which is also referred as current density. The current density of solar cell does not depend on area and for a given sunlight intensity the current density of solar cell is also fixed.

The output voltage of solar cells does not change with the change in solar cell area (A). The output voltage is independent of cell area. Thus, at a given input sunlight intensity, if a 100 cm2 cell produces 0.5 V, then cell of 100 cm2, or 200 cm2 or 50 cm2 or 10 cm2, etc. will produce same 0.5 V.

Calculate new value of output current for solar cells of area 20, 30, 50, 80 and 100 cm2, when current density of cell is 35 mA/cm2.

The current density of a solar cell is its current divided by cell area. The current density is given by the expression.

Here, Jsc  = 35 mA/cm2

So, the expression for the solar cell current can be written as :

Output current ( Isc) =  Jsc X A (mA)  

Now, say, the area of solar cell is 20 cm2, then

Output Current  ( Isc)   = 35 mA/cm2 X 20 cm2 = 700 mA

Similarly, we calculate output current for different values of solar cell area in the table form shown in Table 3.9.

TABLE 3.9 Table for Example 3.11

Current density Jsc   (mA/cm2)	Solar cell area A (cm2)	Output current Isc =  Jsc X A (mA)	Output current Isc (A)
35	20	700	0.70
35	30	1050	1.05
35	50	1750	1.75
35	80	2800	2.80
35	100	3500	3.50

 

So, from above table, it is clear that with increase in area of a solar cell, the amount of output current also increases. Figure 3.8 shows the effect of a solar cell area on the amount of electric current generated by it. 

3.6.4 Change in Angle of Light Falling on Solar cell (Ɵ)

The angle of sunlight with respect to solar cell greatly affects the output power. Solar cell produces maximum power (for given light intensity) when sunlight falls perpendicular to the surface of solar cells. When the light does not perpendicular to solar cells, it always gives less output power than maximum possible output power. This is because when light falls at some angle, some part of light falling on solar cell is less than the amount of light falling on it. So, the output power generated is less when light is not falling perpendicular to solar cell as shown in Figure 3.9. Therefore, one should always try to install a solar cell or module in such a way that most of the time sunlight is close to perpendicular, especially in the afternoon time when the intensity of sunlight is high.

3.6.5 Change in Solar cell Operating Temperature ( T)

The solar cells output voltage, power and efficiency ratings are given at standard test condition (STC = 1000 W/m2 and 250 C ). The cell output voltage, cell efficiency and output power depends on cell temperature. In practical applications, the operating temperature of solar cells may be different than 250 C.  The temperature varies due to ambient temperature and in practice, the solar cells are encapsulated (in PV module) with glass which results in heating of solar cells. Due to encapsulation also solar cell temperature  increases. The change in temperature from standard operating temperature directly affects the output voltage, efficiency and power. Normally, when a solar cell operates at temperature above 250 C temperature; the output voltage, cell efficiency and output power of a solar cell reduces.

The decrease in voltage, power and efficiency with temperature is different for different type of solar cells. For crystalline Si solar cells. For every 10 C increase in temperature above 250 C, the decrease in value of voltage, power and efficiency is given in Table 3.10.

TABLE 3.10 Decrease in value of parameters of crystalline silicon solar cells per 0 C  Rise in Cell Temperature from Standard Test Condition (STC) Value of 250 C 

Parameter of crystalline silicon solar cells	Decrease per 0 C  rise in cell temperature from  Standard Test Condition (STC) value of 25 0 C
Voltage	-0.0023 V or -2.3mV
Power	-0.45%
Efficiency	-0.45%

 

Example 3.12 If the actual operating temperature of the solar cell is  400 C. The output voltage of a solar cell at standard operating temperature is, say 0.7 V. The output voltage decreases by 2.3 mV/0 C. Calculate the new value of output voltage ?

Solution Let us consider, actual operating temperature = Tactual = 400 C.

Standard operating temperature = Tstandard = 250 C.

Output voltage decrease per degree Celsius =Vdecrease = 2.3 mV/ 0 C.

Output voltage at 250 C = Voc (250 C) = 0.7 V

Output voltage at 400 C = Voc (400 C) = ?

 

We know the solar cells output voltage reduces by some value when the temperature is above 250 C.

So, the reduced output voltage = Voc (400 C) = Voc (250 C) – (Vdecrease X ΔT)

ΔT = Tactual  – Tstandard

     = 40 – 25 = 150 C

Now,  0.7 V – (2.3 X  10-3  V/0 C X 150 C = 0.7 V – 0.0345 V

= 0.67 V

So, from the above result, is clear that the solar cells output voltage decreases if operating temperature is above 250 C. Figure 3.10 shows the change in the operating temperature of a solar cell.

Example 3.13 Efficiency of a crystalline silicon solar cell at STC is 15%. What would be its efficiency when cell operating temperature is 600 C ? Refer to Table 3.10.

Solution It is given that the cell is a crystalline silicon cell,

The cell efficiency at STC is; ɳ(STC) =15%,

The cell temperature at STC is 250 C,

The operating temperature of the cell at which efficiency needs to be calculated is 600 C, i.e. we need to calculate ɳ(600 C), i.e. we need to calculate ɳ(600 C).

The difference in operating cell temperature and STC temperature,

ΔT = 60 – 25 = 350 C.

Now considering Table 3.10, the decrease in peak power per degree centigrade is given but not for efficiency . It is a safe to assume that the change in efficiency will be the same as change in peak power of the cell. Therefore, the change in condition (STC) value of  250 C is -45%.

Thus, 

Cell efficiency at 600

Cell efficiency at STC – decrease in cell efficiency due to temperature.

ɳ(600 C) = ɳ(STC) – 0.45% / 0 C of ɳ(STC)

ɳ(STC) – 0.45% / 0 C of ɳ(STC) X ΔT (0 C)

It is clear from the above calculations that the cell efficiency decreases as the cell operating temperature  increases. In practice, the ambient temperature can be higher than the value of temperature in STC. On top of that, in solar PV modules where cells are encapsulated, the cell temperature is normally  higher than the ambient temperature. Thus , in most cases, in moderate to hot climate., cell efficiency is normally  lower than the cell efficiency at STC, which means that the power generated by the cell is normally lower than power generated under STC.

In the above problem, the loss of efficiency due to increase in cell temperature was calculated. In the same way, the loss of generated power (peak power) of the cell with increase in cell temperature can be calculated.    

Worksheet 3.5 : The maximum rated power point of a crystalline silicon solar cell is 2.5 Wp. Calculate the maximum power output at 450C, 550C  and 650C cell operating temperature. For crystalline silicon cell decrease in maximum power per degree centigrade increase in cell temperature, (from STC value of  250C), is -0.45% / 0C. Fill the sheet (Table 3.11).

Use following equation :

Actual Pmax at cell operating temperature (watt)

= Pmax (STC) – 0.45% / 0C X Pmax (STC) X  ΔT (0 C)

TABLE 3.11 To Obtain Missing Quantities

Operating Cell Temperature (0C)	STC cell temperature (0C)	Different in temperature ΔT (0C)	Pmax at STC (watt)	% decrease in power per 0C rise in temperature	Decrease in cell power at operating temperature (watt)	Actual maximum power point at cell operating temperature (watt)
A	B	C	D	E	F = E X D X C	G = D – F
45	25	20	–	-0.45%	–	2.27
55	–	–	2.5	–	0.337	–
65	–	–	–	-0.45%	–	2

 

In section 3.6, we have learned five factors affecting the power generated by solar cells. In addition to these factors, the material used for making any solar cells determines its properties and overall performance. In Chapter 4, we see the effect of different materials used for solar cells.