Chapter 3: Solar Cells 41

3.3 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
How Solar Cell Generates spectrum, there are many photons of different energy. For generation of electricity,
Electricity? photons 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 are 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
at 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 used 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 throughout 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?

3.4 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
Parameters of Solar Cells 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 (Voc) and
 Maximum power point
 Current at maximum power point (Im)
 Voltage at maximum power point (Vm)
 Fill factor (FF)
 Efficiency (h),
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.

Figure 3.4
Schematic of solar cell I-V curve and
its parameters.
42 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

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 this 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  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 suggests, 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.
I ¥ Vm
FF = m
I sc ¥ Voc

Pm
or FF =
I sc ¥ Voc
Here the expression for Pmax or Pm can alternatively be written in terms of
Isc, Voc and FF as:
Pm = Isc  Voc  FF
 Chapter 3: Solar Cells 43

 Efficiency (h): 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:
A solar cell performance depends on Pm I ¥ Voc ¥ FF
its parameters or the cell parameters h= = sc
and determines the performance Pin Pin ¥ A
of a solar cell under the sunlight,
particularly the amount of power it will Let us now see what the possible values of solar cell parameters and how the values
produce in a given condition. 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 100 cm2 at Standard Test
Condition (STC) is given as 35 mA/cm2. Find out the output current of the solar cell.
Solution First, we write the formula for current density of a solar cell given by
I sc
Current density (J sc ) = (mA/cm 2 )
A
where,
Jsc = Current density (mA/cm2)
Isc = Output current (mA)
A = Area (cm2)
Given that, Jsc = 35 mA/cm2
So, the expression for solar cell current can be written as:
Output current (Isc) = Jsc  A (mA)
Now, given that area of solar cell is 100 cm2, then
Output current (Isc) = 35 mA/cm2  100 cm2 = 3500 mA or 3.5 A
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 0.5 V at maximum power point.
What is the maximum power point of the solar cell?
44 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Solution First, we write formula for the maximum power point of a solar cell, given by
Pm or Pmax = Im  Vm
Given that, Im = 0.6 A
Vm = 0.5 V
Therefore, the maximum power point, Pm = 0.6 A  0.5 V = 0.3 W
Example 3.3 A solar cell having an area of 100 cm2 gives 3.1 A current at maximum power
point and 0.5 V at maximum power point at STC. The cell gives 3.5 A short circuit
current and 0.6 V 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  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  0.5 V = 1.55 W
Now, we write the formula for efficiency of a solar cell given by
Pmax
h=
Pin ¥ A
where,
h = Efficiency in per cent (%)
Pmax = Output power in watt (W)
Pin = Light input power per unit area in watt/square meter (W/m2)
A = Solar cell area in square meter (m2)
h= ?
We know, Pm = 1.55 W and at STC, Pin = 1000 W/m2
First, we convert the unit of area from square centimetre (cm2) to square metre
(m ) by dividing area in cm2 by 10000.
2

Here, A = 100 cm2 = 100  10–4 m2 = 0.01 m2

Now, putting the number we can calculate the efficiency of the cell.
Pmax 1.55 watt
h= = ¥ 100 = 15.5%
Pin ¥ A 1000 W/m 2 ¥ 0.01 m 2
From an I-V curve of a solar cell, all
solar cell parameters can be derived. 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.

Figure 3.5
Figure for Example 3.4.
 Chapter 3: Solar Cells 45

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  Vm = 0.40  0.5 = 0.2 W
I m ¥ Vm
Fill Factor, FF =
I sc ¥ Voc
Pm 0.2
or FF = = ¥ 100 = 63.49%
I sc ¥ Voc 0.45 ¥ 0.7
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
0.55 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 max 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  10–4 m2 = 0.0025 m2
Now,
Maximum power point, Pm or Pmax = Im  Vm = 0.85  0.55 = 0.4675 W
I m ¥ Vm
Fill Factor, FF =
I sc ¥ Voc
Pm 0.4675
or FF = = ¥ 100 = 79.91%
I sc ¥ Voc 0.9 ¥ 0.65
Pmax 0.4675
Efficiency (h) = = ¥ 100 = 18.7%
Pin ¥ A 1000 ¥ 0.0025
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 2.5 A current at maximum power
point at STC. The cell gives 3 A short circuit current and 0.5 V open circuit voltage.
What is the voltage at maximum power point of the solar cell?
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
I ¥ Vm
Fill Factor (FF) = m
I sc ¥ Voc
46 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

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 per cent to decimal by dividing it by
100.
60
Therefore, FF = = 0.6
100
Now, we rewrite the formula for Fill Factor of a solar cell to get the value of Vm
given by expression below.
I sc ¥ Voc
Voltage at maximum power point, Vm = FF ¥
Im
Now, putting the value, we can calculate the voltage at maximum power point.
I sc ¥ Voc 3 ¥ 0.5
Vm = FF ¥ = 0.6 ¥ = 0.36 V
Im 2.5
Thus, the voltage at maximum power point is 0.36 V.
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
I m ¥ Vm
Fill Factor (FF) =
I sc ¥ Voc
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 = 68%
First, we convert Fill Factor (FF) from per cent to decimal by dividing it by
100.
68
FF = = 0.68
100
Now, we rewrite formula for Fill Factor of a solar cell to get the value of Im given
by expression below.
 Chapter 3: Solar Cells 47

I sc ¥ Voc
Current at maximum power point, I m = FF ¥
Vm
Now, putting the value, we can calculate the current at maximum power point.
I sc ¥ Voc 3 ¥ 0.7
I m = FF ¥ = 0.68 ¥ = 2.38 A
Vm 0.6
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  Vm
where,
Pm = Maximum power point (W)
Im = Current at maximum power point (A)
Vm = Open circuit voltage (V)
Now, we rewrite formula for maximum power point Pm of a solar cell to get the
value of Im given by expression below.
P
Current at maximum power point, I m = m
Vm
Putting the value, we can calculate the current at maximum power point.
Pm 0.3
Im = = = 0.46 A
Vm 0.65
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  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
The solar cell parameters can be
10 3.19 0.51
extracted by measuring several
current-voltage data points from short 11 3.58 0.46
circuit to open circuit condition. 12 4.33 0.00
48 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

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
3 Current at max power point (Im) Current value at maximum power point
4 Voltage at max power point (Vm) Voltage value at maximum power point
Im ¥ Vm
5 Fill Factor (FF) =
Isc ¥ Voc

Voc ¥ Isc ¥ FF
6 Efficiency =
Pin ¥ A

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

Table 3.4 To 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 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
Solar Cell Technologies depends on the name the material used in that particular technology. The properties
of materials used in different type of solar cells are different. Hence, different types
of solar cells have different values of solar cell parameters like efficiency (h),
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 h, A, Jsc, Voc
and FF are mentioned in Table 3.6.
 Chapter 3: Solar Cells 49

Table 3.5 Commercial Solar Cells Technology, Materials and Efficiency

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

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

Table 3.6 Typical Solar Cell Parameters (h, Jsc, Voc and FF) of Commercial Solar Cells with Available Cell Areas

Solar cell type Efficiency (h) Cell area (A) Output voltage (Voc ) Output current (Jsc ) Fill factor (FF)
(in %) (in cm2) (in V) (in mA/cm2) (in %)
Mono-crystalline silicon 14 – 17 5 – 156 0.55 – 0.68 V 30 – 38 70 – 78
Poly or multi-crystalline 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 8 – 11 5 – 200 0.50 – 0.7 V 20 – 30 60 – 70
(CIGS)
Gallium indium phosphide/Gallium 30 – 35 1–4 1.0 – 2.5 V 15 – 35 70 – 85
arsenide/Germanium (GaInP/
GaAs/Ge)

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

3.6 There are five common factors that affect the power generated by solar cells. They
are as follows:
Factors Affecting 1. The conversion efficiency (h),
Electricity Generated by a 2. The amount of light (Pin),
Solar Cell 3. The solar cell area (A),
4. The angle at which day light falls (q ), and
5. The operating temperature (T )

3.6.1 Of the total light energy falling on a solar cell, only some fraction of the light
Effect of Conversion 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
Efficiency (h) 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 (h) of solar cell
can be given as:
Pout
h= or Pout = Pin ¥ h ¥ A
Pin ¥ A
50 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

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 or W/cm2 and unit of cell area is in m2 or cm2. The solar cell
More efficient solar cell produces more efficiency is given for standard test condition (STC) and under the STC, the value
power from the same area. of input power density, Pin is taken as 1000 W/m2 or 0.1 W/cm2.

Example 3.9 Calculate the output power from a solar cell 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 efficiency of a solar cell given by
Pout
h= or Pout = Pin ¥ h ¥ A
Pin ¥ A
where,
h = Efficiency in per cent (%)
Pout or Pmax = Output power in watt (W)
Pin = Light input power per unit area in watt/metre2 (W/m2)
A = Solar cell area in metre2 (m2)
h = 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  10– 4 m2
Now, we solve for solar cell of efficiency 30%
Above equation can be written as:
Pmax = h  Pin  A
We put the respective terms values and we get,
Ê 30 ˆ
Pmax = Á ¥ 1000 ¥ 100 ¥ 10 -4 = 3 W
Ë 100 ˜¯
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

h (%) Pin (W/m2) A (cm2) A (m2) h /100 Pmax = (h /100)  Pin  A (W)
30 1000 100 0.01 0.30 3.0
24 1000 100 0.01 0.24 2.4
19 1000 100 0.01 0.19 1.9
A solar cell with double efficiency will
16 1000 100 0.01 0.16 1.6
give double power output from same
area. 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.
 Chapter 3: Solar Cells 51

Figure 3.6
The effect of solar cells conversion
efficiency on the output power for
solar cell of 100 cm2 area.

3.6.2 We should keep in mind that the amount of sunlight (intensity of sunlight) falling on
Change in the Amount of 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
Input Light (Pin) 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 ½ 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  Voltage) by solar cell is proportional
to the amount of light falling on it. The amount of power generated by the solar
Large amount of light falling means cells throughout the day keeps changing (i.e., it is not constant). So, a solar cell
high generated power, less amount
of light falling means low generated gives high power when the intensity of light falling is high. Similarly, less power
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 solar cell is 100 cm2.
Solution First we write formula for efficiency of a solar cell given by
Pmax
h=
Pin ¥ A
where,
h = Efficiency in per cent (%)
Pmax = Output power in watt (W)
Pin = Light input power per unit area in watt/meter (W/m2)
A = Solar cell area in square metre (m2)
h = 16%
Pin = 1000, 800, 400 W/m2
Pmax = ?
It is given that cell efficiency is 16% and cell area is A = 100 cm2.
52 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

First, we convert area unit from square centimetre (cm2) to square metre (m2)
by dividing area in cm2 by 10000.
A = 100 cm2 = 100  10–4 m2
Now, we solve for light input power = 1000 W/m2
Above equation can be written as:
Pmax = h ¥ Pin ¥ A
We put the respective terms values and we get,
Ê 16 ˆ
Pmax = Á ¥ 1000 ¥ 100 ¥ 10 -4 = 1.6 W
Ë 100 ˜¯
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

h (%) Pin (W/m2) A (cm2) A (m2) h /100 Pmax = (h /100)  Pin  A (W)
16 1000 100 0.01 0.16 1.60
16 0800 100 0.01 0.16 1.28
A solar cell with double light power
16 0600 100 0.01 0.16 0.96
input will produce double electrical
power output from same area. 16 0400 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.

Figure 3.7
The effect of amount of light (light
intensity) falling on solar cell on the
output power for solar cell of 100 cm2
area and 16% efficiency.

3.6.3 The amount of maximum output current (Isc or short circuit current) of a solar cells
Change in Solar Cell 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
Area (A) by it will be large. Similarly, less amount of electric current will be 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 is given in units
of A/cm2 or mA/cm2. 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.
 Chapter 3: Solar Cells 53

Current density (Jsc) of a solar cell is

always fixed or constant.
The output voltage of solar cells does not change with the change in solar cell area
Large solar cell area means high (A). The output voltage is independent of cell area. Thus, at a given input sunlight
current, small solar cell area means intensity, if a 100 cm2 cell produces 0.5 V, then cell of 100 cm2, or 200 cm2 or
low current. 50 cm2 or 10 cm2, etc. will produce same 0.5 V.
Example 3.11 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.
Solution The current density of a solar cell is its current divided by cell area. The current
density is given by the expression
I
Current density (J sc ) = sc (mA/cm 2 )
A
Here, Jsc = 35 mA/cm2
So, the expression for the solar cell current can be written as:
Output current (Isc) = Jsc  A (mA)
Now, say, the area of solar cell is 20 cm2, then
Output current (Isc) = 35 mA/cm2  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 × A (mA) Output Current Isc (A)
35 020 0700 0.70
35 030 1050 1.05
35 050 1750 1.75
35 080 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 solar cell area on
the amount of electric current generated by it.

Figure 3.8
The effect of cell area on the output
current for same light intensity and
efficiency of the cell.

3.6.4 The angle of sunlight with respect to solar cell greatly affects the output power.
Change in Angle of Light 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
Falling on Solar Cell (q ) 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 reflected. Hence, the actual light utilized by a solar cell is less than the
amount of light falling on it. So, the output power generated is less when light is
54 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

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
Light falling perpendicular to solar cell sunlight is close to perpendicular, especially in the afternoon time when the intensity
gives maximum output power. of sunlight is high.

Figure 3.9
The effect of the angle of sunlight
falling on a solar cells on output
power of cells.
For any solar cell, the output voltage
is always constant. It is independent
of solar cell area, the amount and
angle of light falling on solar cell.

3.6.5 The solar cells output voltage, power and efficiency ratings are given at standard test
Change in Solar Cell condition (STC = 1000 W/m2 and 25°C). The cell output voltage, cell efficiency and
output power depends on cell temperature. In practical applications, the operating
Operating Temperature (T ) temperature of solar cells may be different than 25°C. The cell 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 25°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 1°C increase in
temperature above 25°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 °C Rise in Cell Temperature from Standard Test Condition (STC) Value of 25°C
For a solar cell, higher temperature Parameter of crystalline silicon solar cells Decrease per °C rise in cell temperature from
means lower power output. standard test condition (STC) value of 25 °C
For typical Silicon solar cell the Voltage – 0.0023 V or –2.3 mV
output voltage decreases by 2.3 mV
Power – 0.45%
per degree centigrade increase in
temperature. Efficiency – 0.45%

Example 3.12 If the actual operating temperature of the solar cell is 40 °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/°C. Calculate the new value of output voltage?
Solution Let us consider, actual operating temperature = Tactual = 40 °C
Standard operating temperature = Tstandard = 25 °C
Output voltage decrease per degree Celsius = Vdecrease = 2.3 mV/°C
Output voltage at 25 °C = Voc (25 °C) = 0.7 V
Output voltage at 40 °C = Voc (40 °C) = ?
 Chapter 3: Solar Cells 55

We know the solar cells output voltage reduces by some value when the temperature
is above 25 °C.
So, the reduced output voltage = Voc (40 °C) = Voc (25 °C) – (Vdecrease  DT )
DT = Tactual – Tstandard
= 40 – 25 = 15 °C
Now, 0.7 V – (2.3  10–3 V/°C  15 °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 25 °C. Figure 3.10 shows the change in the output
voltage with 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 60 °C? Refer to Table 3.10.
Solution It is given that the cell is a crystalline silicon cell,
The cell efficiency at STC is; h(STC) = 15%,
The cell temperature at STC is 25 °C,
The operating temperature of the cell at which efficiency needs to be calculated is
60 °C, i.e. we need to calculate h(60 °C).
The difference in operating cell temperature and STC temperature,
DT = 60 – 25 = 35 °C.
Now considering Table 3.10, the decrease in peak power per degree centigrade
is given but not for efficiency. It is safe to assume that the change in efficiency
will be the same as change in peak power of the cell. Therefore, the change in
efficiency (h) per degree centigrade rise in cell temperature from standard test
condition (STC) value of 25°C is – 45%.
Thus,
   Cell efficiency at 60°C
= cell efficiency at STC – decrease in cell efficiency due to temperature  
h (60 °C) = h (STC) - 0.45 %/°C of h (STC)
= h (STC) - 0.45 %/°C ¥ h (STC) ¥ DT (°C)
0.45
= 15 - ¥ 15 ¥ 35 = 15 - 2.36 = 12.63%
100
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.
56 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Figure 3.10
The effect of change in solar cell
operating temperature on voltage
output of a solar cell.

Worksheet 3.5: The maximum rated power point of a crystalline silicon solar cell is 2.5 Wp. Calculate
the maximum power output at 45 °C, 55 °C, and 65 °C cell operating temperatures. For crystalline silicon cell
decrease in maximum power per degree centigrade increase in cell temperature, (from STC value of 25 °C),
is –0.45%/°C. Fill the sheet (Table 3.11).
Use following equation:
Actual Pmax at cell operating temperature (watt)
= Pmax (STC) - 0.45 %/°C ¥ Pmax (STC) ¥ DT (°C)
0.45
= Pmax (STC) - ¥ Pmax (STC) ¥ DT
100
Table 3.11 To Obtain Missing Quantities

Operating cell STC cell Different in Pmax at STC % decrease in Decrease in cell Actual maximum power
temperature temperature temperature DT (watt) power per °C rise power at operating point at cell operating
(°C) (°C) (°C) in temperature temperature (watt) temperature (watt)
A B C D E F = E × D × C G = D – F
45 25 20 – – 0.45% – 2.27
55 – – 2.5 – 0.337 –
65 – – – – 0.45% – –

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.
 Chapter 4: Solar PV Modules 71

Fill in the parameter of PV module (Table 4.7) using the measured I-V points given
in Table 4.6.
Table 4.7 Parameters of PV Modules

S. No. Parameters Values of parameter Unit of parameter

1 Short circuit current (Isc)
2 Open circuit voltage (Voc)
3 Maximum power point, Pm
4 Current at maximum power point (Im)
5 Voltage at maximum power point (Vm)
6 Fill factor (FF)
7 Efficiency

4.4 Let us now discuss how in practical applications the PV module power output
varies with variation in ambient conditions like temperature, solar radiation, angle
Factors Affecting Electricity of sunrays, etc. The change in PV module parameter output power with change in
Generated by a Solar PV ambient condition is important to understand. This will be useful in estimating the
Module possible generation of electricity using solar PV modules and possible performance
of PV systems in a given condition.
There are five common factors affecting the power generated by solar modules.
These factors are listed below and discussed in detail in the following sections:
1. The conversion efficiency (h)
2. The amount of light (Pin)
3. The operating temperature (T )
4. The solar cell area (A), and
5. The angle at which day light falls (q )

4.4.1 The modules consist of several cells electrically interconnected to each other in series
Effect of Conversion or/and parallel. A solar cell converts some fraction of light energy falling on it into
electrical energy. In this way, a PV module also converts only some portion of the
Efficiency (h) total light falling on it into electrical energy. The ratio of electrical energy generated
to the input light energy is referred as conversion efficiency of PV modules. The
efficiency of modules is always less than the efficiency of solar cells used in it.
All solar cells used in PV modules may not be perfectly identical, that is, all
the parameters of solar cells may not be exactly identical. Difference in solar cells
used in PV modules results in less power generation when connected in modules (as
compared to the case when all cells work individually, as discussed in Section 4.1).
Also, the module area is always larger than the total cells area as the spacing
area between the cells is considered (shown in Figure 4.10). The area considered
for the calculation of efficiency affects the conversion efficiency. The conversion
efficiency of module basically depends on the solar cells used and the method used
for interconnecting them. In a module, the cells can be inter-connected in series
or parallel combination. Once a module is assembled, its efficiency value becomes
fixed and it generally does not change.
The efficiency of a module is given in terms of maximum power (Pmax) or
peak power (Pm) that module can generate for a given input solar radiation. The
Pmax output or Pm output of module depends on voltage developed across module
terminal and current it can supply. In a module, the type of cells inter-connection
greatly affects the output power. If the instantaneous solar radiation or power density
is Pin, the expression for the efficiency (h) of module can be given as:
72 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Figure 4.10
Showing solar cell area and spacing
area between cells in a module.

Pm
h= or Pm = Pin ¥ h ¥ A (4.5)
Pin ¥ A
For given input power, the value of the output power is directly determined by the
value of module’s conversion efficiency and module area. The modules with higher
efficiency values will always give better performance. Similar to solar cells, the unit
of module efficiency is percentage (%), the unit of Pm is normally watt, the unit
of Pin is normally W/m2 or W/cm2 and the unit of module area is m2 or cm2. The
module 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/cm2.

Example 4.9 Calculate the output power from a module if its efficiency (in %) is 22, 17, 16 and
12, input power density is 1000 W/m2 and area of module is 58.7 inch by 39.0 inch.
Solution First, we write formula for efficiency of a solar cell given by the expression
Pm
h= (%)
Pin ¥ A
where
h= Efficiency in percent (%)
Pm or Pmax = Output power in watt (W)
Pin = Light input power per unit area in watt/metre2 (W/m2)
A= Solar cell area in metre2 (m2)
h= 22, 17, 16, 12 (in %)
Pin = 1000 W/m2
A= 58.7  39.0 (inch)2
Pm = ?
First, we convert cell area from (inch)2 to m2
We know, 1 inch = 0.0254 metres
58.7 inch = 1.49 metre and 39.0 inch = 0.99 metre
Therefore, module area (A) = 1.49  0.99 = 1.475 m2
Now, we solve for solar cell of efficiency 22 %.
 Chapter 4: Solar PV Modules 73

Above equation can be written as:

Pm = h  Pin  A
We put the respective terms values and we get,
Ê 22 ˆ
Pm = Á ¥ 1000 ¥ 1.475 = 324.5 W
Ë 100 ˜¯
Similarly, we calculate output power for other efficiencies in the table form as
shown in Table 4.8.
Table 4.8 Table for Example 4.9

h (%) Pin (W/m2) A (inch)2 A (m2) h/100 Pm = (h /100) × Pin × A (W)

22 1000 2289.3 1.475 0.22 324.50
17 1000 2289.3 1.475 0.19 250.75
16 1000 2289.3 1.475 0.16 236.00
12 1000 2289.3 1.475 0.12 177.00

From the above table it clear that when efficiency of a module reduces the output
power generated also reduces. The output power of module directly depends on the
efficiency of module as shown in Figure 4.11.

Figure 4.11
The effect of module conversion
efficiency on the output power for
module of 1.475 m2 area.

4.4.2 We should keep in mind that the amount of sunlight (intensity of sunlight), falling on
Change in the Amount of solar PV module keeps changing from morning to evening. The current and voltage
output of a solar PV module depends on the amount of light falling on it. The electric
Input Light (Pin ) current generated by solar PV is directly proportional to the amount of light falling
74 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

on it. Suppose, a solar PV module produces 5 A current under 1000 W/m2 input
solar radiation, then under 500 W/m2 input solar radiation, the PV module will only
produce 2.5 A current (because input radiation is half). As the amount of sunlight
falling on solar PV module increases from morning till afternoon, the current output
of a solar PV module also increases from morning till afternoon. From afternoon till
evening, the amount of sunlight falling on a solar PV module decreases, and hence
the current output of a solar PV module also decreases from afternoon till evening.
The output voltage of a solar PV module is not affected strongly by change in the
amount of light. If a solar PV module produces 20 V at noon time, its voltage will
roughly remain same in the morning as well as evening hours.
The solar PV module current output is proportional to the amount of solar
radiation and voltage is relatively not affected by variation in the sunlight intensity.
Therefore, the amount of power generated (Power = Current  Voltage) by solar PV
module is proportional to the amount of light falling on it. The amount of power
generated by the solar PV modules throughout the day keeps changing (i.e., it is
not constant). So, a solar PV module gives high power when the intensity of light
falling is high. Similarly, less power is generated when the intensity of light falling
is low. An example of a 75 Wp (or 75 Wmax or 75 Wm) PV module is shown in
Figure 4.12. The expected power output of the 75 Wp PV module under various
input solar radiation intensity is given, including the PV module power output
under STC. The corresponding I-V characteristics of the same PV module, for 25 °C
cell temperature and for various solar radiation intensity (1000 W/m2, 800 W/m2,
600 W/m2, 400 W/m2 and 200 W/m2) are also given in Figure 4.12. Please note
here that the power output under various solar radiation conditions given in
Table 4.9 and in Figure 4.12 are the peak power output in that condition. Peak
Large amount of light falling means power or maximum power point is shown by ‘’ in Figure 4.12. The actual power
high generated power, less amount output from a PV module may be lower than the maximum power point, if the PV
of light falling means low generated module is not operating at current and voltage corresponding to maximum power
power by the solar PV module.
point (as discussed in Section 3.2.1).

Figure 4.12
I-V characteristics of a 75 Wp (STC
condition) PV module under various
input solar intensities (The peak
power of the module under various
solar radiation intensities is also
mentioned).

Table 4.9 Expected Output Power of a 75 Wp PV Module Under Various Solar Radiation Intensity.
(Temperature of the PV Module is Assumed to be Constant in all Conditions)

Amount of light input or sunlight intensity (Pin) (W/m2) Peak power output of a PV module (Wp) (watt)
1000 (STC) 75 (STC)
800 60
600 45
400 30
200 15
 Chapter 4: Solar PV Modules 75

A solar PV module with double light power input will produce double electrical
power output.
Example 4.10 A Wp rating of a PV module is 230 Wp (or 230 Wmax) under STC. What will be the
output power of the PV module if the solar radiation intensity is only 400 W/m2?
Assume the temperature of the cells module remain the same in both conditions.
Solution It is given that peak power rating is 230 Wp.
Given, solar radiation condition is STC, which is equivalent to 1000 W/m2 input
power.
Now, we know that the PV output power varies linearly with the input sunlight
intensity (when cell temperature is constant, which is given). In this way, at 1000 W/m2
input power, if the peak output power is 230 Wp, then at 1000 W/m2 input power,
the peak output power will be
230 Wp
2
¥ 400 W/m 2 = 92 Wp
1000 W/m
Example 4.11 A solar PV module’s maximum power output at 300 W/m2 and 700 W/m2 is
42 watt and 98 watt respectively. What will be the PV Wp rating of the module
under STC? Assume the temperature of the cells module remain the same in both
conditions.
Solution It is given that at 300 W/m2, maximum output power is 42 watt, and at 700 W/m2,
maximum output power is 98 watt.
Since the cell temperature is constant, the PV module’s maximum power output
at any solar radiation condition will linearly depend on the solar radiation power
input.
We need to find out the peak power output of the PV module under STC, which
means under 1000 W/m2 solar radiation condition.
We can write; at 300 W/m2 input power, the peak output power is 42 Wp, then
at 1000 W/m2 input power, the peak output power will be
42 Wp
¥ 1000 W/m 2 = 140 Wp
300 W/m 2
Also, we can write; at 700 W/m2 input power, the peak output power is 98 Wp,
then at 1000 W/m2 input power, the peak output power will be
98 Wp
¥ 1000 W/m 2 = 140 Wp
700 W/m 2
4.4.3 The solar PV modules output voltage, power and efficiency ratings are given at
Effect of Change in PV standard test condition (STC = 1000 W/m2 and 25 °C). The PV module output
voltage, PV module efficiency and output power depends on cell temperature
Module Temperature in PV module. In practical applications, the operating temperature of solar cells
in PV modules may be different than 25 °C. The cell temperature varies due to
ambient temperature. In many cases, the ambient temperature is higher than the
STC temperature of 25 °C. Moreover, in practice, the cells in a PV module are
encapsulated with glass cover. The presence of glass cover has a greenhouse effect,
which results in heating of solar cells and increase in their temperature. The change
in temperature from standard operating temperature directly affects the output voltage
of a PV module. With increase in cell temperature in PV modules, the voltage output
of PV module decreases, which results in decrease in PV module efficiency and
PV module output power.
76 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

The change in PV module parameters with increase in cell’s operating

temperature (or temperature coefficient of PV module parameters) in PV module is
given in Table 4.6. The different values of module output at different temperatures.
The short circuit current of PV module increases with increase in cell temperature,
while the other parameters like open circuit voltage, efficiency and output power
decreases with increase in cell temperature in PV modules. Change in parameters
value with temperature for crystalline silicon, cadmium telluride and amorphous
silicon is given in Table 4.10.

Table 4.10 Typical Value of Change in Parameter Value Per °C Rise in Cell Temperature From Standard Test Condition
(STC) Value of 25 °C (The PV module parameters of various commercially available technologies are given)

PV Technology name Typical value of change in parameter value per °C rise in cell temperature from standard test condition
(STC) value of 25 °C (+ indicates increase, – indicates decrease)
Temperature coefficient Temperature coefficient Temperature coefficient Temperature coefficient
of current (Isc) of voltage (Voc) of fill factor (FF) of power (Pm)
Crystalline silicon +0.08%/°C – 0.35%/°C –0.15%/°C – 0.45%/°C
Cadmium telluride +0.04%/°C – 0.25%/°C – 0.035%/°C – 0.25%/°C
Double junction +0.07%/°C – 0.3%/°C –0.095%/°C – 0.25%/°C
amorphous silicon

Note: The temperature coefficient of parameters are given as percentage of parameter value at STC. The values given in this table
are typical values of the parameter, the actual value may be different from one manufacturer to other.

Normally, the Wp rating of PV module is one of the most important parameters. In

real-life situation, due to higher cell operating temperature than the STC temperature,
the actual maximum output power of modules is lower than STC value. Using
the temperature coefficient of the module parameter, the change in value of
parameter with increase in temperature can be estimated. In this way, if we know
the temperature coefficient of power, we can calculate how much will be drop in
peak power output of a PV module in real-life operating condition.
The temperature coefficient of parameters is given in percentage of parameter
value at STC. Thus, following formulae can be written to find out the change in
parameter value as compared to STC value due to increase in temperature:

In terms of formula, we can write as:

For a solar PV module, higher tempera-
P(temp) = P(STC) – TC  P(STC)  DT
ture means lower power output. For a Using the above formulae, one can find the change in any parameter value for
typical crystalline silicon PV module,
the output voltage decreases by any given cell operating temperature. The above formula can be written for any
0.35% per degree centigrade rise in parameter. For instance, the formulae for change in maximum module voltage due
temperature. to increase in cell temperature in PV module will be given as:
Vm, (temp) = Vm, (STC) – TCvoltage  Vm, (STC)  DT
 Chapter 4: Solar PV Modules 77

The change in module’s maximum power output due to increase in cell temperature
in PV module will be given as:
Pmax, (temp) = Pmax, (STC) – TCpower  Pmax, ((STC)  DT

Table 4.11 Different Values of Module Output at Different Temperatures

S. No. Temperature (°C) Wattage (watts)

1 25 (STC) 75.0
2 30 73.30
3 40 69.90
4 50 66.60
5 60 63.20
6 70 59.80

Worksheet 4.4: The maximum rated power point of a crystalline silicon solar cell is 75 Wp. Calculate
the maximum power output at 45 °C, 55 °C, and 65 °C cell operating temperature. For crystalline silicon, cell
decrease in maximum power per degree centigrade increase in cell temperature, (from STC value of 25 °C),
is – 0.45%/ °C. Fill Table 4.12.
Use the following equation:
Actual Pmax at cell operating temperature (watt)
Pmax, (temp) = Pmax, (STC) – TCpower  Pmax, (STC)  DT

Table 4.12 Change in Wattage of Module due to Change in Temperature

Operating cell STC cell DT (°C) Pmax, (STC) (watt) TC (%) TCpower  Pmax, (STC)  DT Pmax, (temp) (watt)
temperature (°C) temperature (°C) (watt)
45 25 20 – – 0.45 – –
55 – – 75 – – 64.87
65 – – – – 0.45 – –

Example 4.12 Voltage at maximum power point (Vm) of a crystalline silicon solar PV module at
STC is 17 V. What would be the voltage when PV module operating temperature
is 60 °C? Refer to Table 4.10.
Solution It is given that the PV module is a crystalline silicon PV module.
The PV module voltage at maximum power point at STC is
Vm, (STC) = 17 V
The PV module temperature at STC is 25 °C.
The operating temperature of the PV module at which Vm needs to be calculated
is 60 °C, i.e., we need to calculate Vm, (60 °C).
The difference in operating PV module temperature and STC temperature
DT = 60 – 25 = 35 °C
Now, considering Table 4.10 the decrease in voltage per degree centigrade rise
in PV module temperature from standard test condition (STC) value of 25 °C is
– 0.35%.
78 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Now, using the formulae for estimating change in the voltage due to temperature
increase
Vm, (temp) = Vm, (STC) - TCvoltage ¥ Vm, (STC) ¥ DT
0.35
= 17 - ¥ 17 ¥ 35 = 17 - 2.08 = 14.91 V
100

4.4.4 Generally, the modules of a large area give high power compared to the modules
Change in PV Module of a small area. It is very important to understand the reason behind it. When we
say the area of a module has increased or decreased, it means the area of module
Area (A) increases or decreases with the increase or decrease in the number of cells in a
Large number of cells in a module
module. For example in a module there are 36 cells and the area of each cell is
means large module area; Small 156 cm2 then total area of 36 cells = 36 × 156 = 562 cm2 = 0.562 m2. Now, if the
number of cells in a module means number of cells in same module is increased to say 72 cells then the total area of
small module area.
cells becomes 1.12 m2 (i.e., double of 0.562 m2).
Now, we need to understand how change in area of a module is related to the
change in maximum output power (Pm) of a module. We have learned in the Section
4.3.3 of this chapter that the maximum output power of a module depends on the
maximum output current (Im) and the maximum output voltage (Vm). For example,
if at STC module of area 1.475 m2 having Vm = 26 V and Im = 6.73 A gives
Pm = 175 W then a module of area 2.950 m2 having Vm = 52 V and Im = 6.73 A
will give Pm = 350 W under same input sunlight intensity (shown in Figure 4.13).

Figure 4.13
The effect of module area on the
output current for same light intensity
and efficiency of the module.

From above example, the question arises; why has the output voltage and output
power doubled with the increase in module area? This is because Vm and Im of
modules depend on the series or parallel types of cells inter-connectivity used. When
 Chapter 4: Solar PV Modules 79

strings of cells are connected in series, the voltage is additive and current is fixed
(i.e., current of a single string of cells). When the strings of cells are connected in
parallel, the current is additive and voltage is fixed (i.e., voltage of a single string of
cells). So, when the strings of cells in a module are inter-connected in series, high
output voltage is obtained. When the strings of cells in a module are inter-connected
in parallel, high output current is obtained. Let us consider a module of area 2.95 cm2
that consists of two units of 1.475 m2 area in which the cells are connected in
series to give high Vm = 26 V and Im = 6.73 A at STC (Pm = 175 W) as shown in
Figure 4.13). These units of 1.475 m2 are connected in parallel to give Vm = 26 V
and high current Im = 13.46 A at STC (Pm = 350 W) as shown in Figure 4.14. So,
for practical applications, it doesn’t matter in which way the cells or the strings of
cells are inter-connected in a module. Here, change in area is mainly due to increase
or decrease in the number of cells in a module. It is important to understand that
with the change in the area of module, the output power of the modules also changes.

Figure 4.14
(a) Module with single string of cells
and (b) Module with two strings of
cells connected in parallel type of
connection.
Large module area means high power
and small module area means low
power.

In Table 4.13, it can be seen that as the area of module (i.e., no. of cells in module)
increases the power of the modules also increases.
Table 4.13 Comparsion of Commercially Available Modules of Different Wattages at Stc
Along with A, Im, Vm and n Respectively

Module 1 Module 2 Module 3 Module 4

Power (Pm) 115 Wp 175 Wp 230 Wp 230 Wp
Area (A) 0.882 m2 1.476 m2 1.646 m2 1.646 m2
Maximum current (Im) 6.76 A 6.73 A 7.93 A 13.64 A
Maximum Voltage (Vm) 17 V 26 V 29 V 17 V
Number of cells (n) 36 54 60 72
80 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

4.4.5 Similar to the solar cells discussed in Chapter 3, the angle of sunlight with respect
Change in Angle of Light to module greatly affects the output power. The modules produce maximum power
(for given light intensity) when sunlight falls perpendicular to the surface of a
Falling on PV Module (q ) module. When the light does not fall perpendicular on the module, 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 module is reflected. Hence, the
actual light utilized by a module is less than the amount of light falling on it. So, the
output power generated is less when light is not falling perpendicular to module as
shown in Figure 4.15. Therefore, one should always try to install a module in such
Light falling perpendicular to modules a way (i.e., angle of module inclination) that most of the time sunlight is close to
gives maximum output power.
perpendicular, especially in the afternoon time when the intensity of sunlight is high.

Figure 4.15
The effect of the angle of sunlight
falling on a module on output power
of module (a) light is at an angle less
than 90°, (b) light is at an angle of 90°
and (c) light is falling parallel.

4.5 The module parameters mentioned in Section 4.3 can also be measured or calculated
based on some measured parameters. The parameters that can be measured by means
Measuring Module of the measuring devices like open circuit and maximum voltage, short circuit and
Parameters maximum current and parameters which can be calculated using measured parameters
are Fill Factor, maximum power point and efficiency. For measuring the module
parameters, following equipments are required:
1. Ammeter or a multimeter
2. Voltmeter or a multimeter
3. Rheostat
4. Connecting wires

4.5.1 The open circuit voltage (Voc) and short circuit current (Isc) can be directly measured
Measuring Voc and Isc with multimeter. For measuring Voc, multimeter in voltmeter mode or a voltmeter
can be used. For measuring Isc, a multimeter in DC current mode or an ammeter
can be used.
Voc measurement When you are measuring Voc or open circuit voltage of a module, there should not
be any load connected to the module, and it should be in open circuit condition.
For measuring Voc, first set the multimeter knob to voltage measurement and set the
range of voltage according to the given module (normally 6 V, 12 V, 24 V, etc.).
Then connect the two terminals of multimeter/voltmeter across two terminals of a
SPV module directly as shown in Figure 4.16. Ensure that the terminals of same
polarity of multimeter and module are connected together. In this arrangement, the
reading shown by the multimeter/voltmeter is open circuit voltage of the given SPV
module. If a negative sign is shown in the meter with reading, it indicates that the
appropriate polarity of the module terminal and meter terminal is not connected.
Reverse the connection and then measure again.
 Chapter 5: Solar PV Module Arrays 91

5.1 Do you remember from Chapter 4, why solar cells are connected in series in a PV
module? If you recall, the main reason for connecting cells in series is to increase
Connection of Modules in the output voltage of a PV module up to certain level, for instance, up to 15 V at
Series maximum power point. Normally, the standard maximum voltages of modules are 15 V,
30 V and 45 V. There are possibilities when the PV system voltage requirement
may be higher than what a single PV module can provide. Thus, in the case when
PV system (a PV power plant and standalone PV system) voltage requirement is
more than the maximum voltage delivered by a single PV module, two or more PV
modules are connected in series. The series connection of PV modules is similar to
the series connection of solar cells in a PV module. Note that, in making a series
If PV modules are connected in series, connection of PV modules, it is not only the PV module voltage that increases but
then their voltage gets added up.
also the total PV power generated also increases.
Series combination of the PV modules is achieved by connecting the opposite
polarity terminals of modules together as shown below in Figure 5.5. The negative
terminal of one module is connected with the positive terminal of the other module.
When two modules with open circuit voltage of Voc1 and Voc2 are connected in series,
the voltage of series combination is the addition of two voltages, which is Voc1 +
Voc2 (as shown in Figure 5.5(a)). Here, the description is given for open circuit
voltages. The concept of addition of voltages in series connected PV modules is
also applicable for other voltages, like Vm, the voltage at maximum power point.
An example of two PV modules with series connection is given in Table 5.1.
Series connection of PV modules When PV modules are connected in series, the voltage of the series connected
is obtained by connecting positive PV modules is the sum of the voltages of individual PV modules.
terminal of one module to negative In the same way (as in Table 5.1), the voltage at maximum power point, Vm,
terminal of the next module.
of the PV modules can also be added.
Table 5.1 An Example of Summation of Open Circuit Voltages of Two Series Connected PV Modules
(Note: Combination of Current Remains Same as that of Single Module)

Open circuit voltage of module 1 Voc1 18 V

Open circuit voltage of module 2 Voc2 18 V
Open circuit voltage of modules connected in series Voc = Voc1 + Voc2 = 18 + 18 = 36 V

When three modules with open circuit voltage of Voc1, Voc2 and Voc3 are connected
in series, the total voltage of series combination will be the sum of these three
voltages, i.e., Voc1 + Voc2 + Voc3 [as shown in Figure 5.5(b)].

Figure 5.5
Series connection of (a) two modules,
and (b) three modules.
92 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Worksheet 5.1: Find out the total open circuit voltage of three PV modules connected in series. Open
circuit voltage of individual module is specified in Table 5.2.
Table 5.2 Open Circuit Voltage Modules

Open circuit voltage of module 1 Voc1 18 V

Open circuit voltage of module 2 Voc2 17.5 V
Open circuit voltage of module 3 Voc3 17.9 V
Open circuit voltage of modules connected in series Voc = Voc1 + Voc2 + Voc3
= 18 + _____ + _____ = _____ V

5.1.1 It is mentioned in the earlier sections that PV modules are connected in series in
Estimating Number of PV order to increase the voltage. The series connection of PV modules is called ‘PV
module string’ or if, in a PV system, the modules are connected only in series,
Modules Required in Series then we can call the series connection of PV modules as ‘PV modules array’. In
and Their Total Power the series connection, the voltage of the PV modules gets added while the current
of the series connected modules remain the same as that of an individual module.
This is assuming that all the PV modules are identical, having identical parameters
like Voc, Vm, Isc and Im.
Now, let us calculate the number of modules which are required to be connected
in a series if the requirement of voltage of PV modules array is known. Also, we
should be able to estimate the total power that the series connected PV modules
will be generating. This exercise can be done in three steps:
Step 1 Note down the voltage requirement of series connected PV modules:
Since the idea is to connect PV modules in series to increase the voltage of array.
How much voltage is required from PV module array should be noted as follows:
PV module parameter Symbol Value Unit
PV module array open circuit voltage Voca volt
PV module array at maximum power point Vma volt

Step 2 Note down the parameter of a PV module that is to be connected

in series: Since in operation, it is expected that a PV module operates under
maximum power point condition, therefore, current and voltage at maximum power
point, that is, Vm and Im of the available PV module (or PV module specified by
client) must be noted. Other PV module information like Voc, Isc and Pm can also
be noted in the following table:

PV module parameter Symbol Value Unit

Open circuit voltage of module Voc volt
Short circuit current of PV module Isc ampere
Voltage at maximum power point Vm volt
Current at maximum power point Im ampere
Maximum power of PV module Pm watt

Step 3 Estimating the number of PV modules to be connected in series: In

order to find out the number of PV modules to be connected in series, total array
voltage is divided by the voltage of individual modules. Since in real time, PV
modules are supposed to work under maximum power point condition, the ratio
of Vma to Vm (array module voltage to module voltage at maximum power point)
should be taken as follows:
 Chapter 5: Solar PV Module Arrays 93

PV module parameter Symbol Value Unit

Required PV array voltage at maximum power Vma volt
point
Voltage at maximum power point of single PV Vm volt
module
Ns =
Number of PV modules in series, Ns number
(Vma /Vm)
Current at maximum power point of PV array Ima = Im
The number of PV modules connected
in series depends on the amount of
voltage required from a PV module
If the ratio of Vma to Vm is not an integer, then the next integer value should be
string. taken. For instance, if the ratio is 3.5. We know that number of modules cannot be
Current of a PV module string is the
3.5, it can be either 3 or 4. Therefore, in this case, the next integer number, i.e.,
same as the current of individual PV 4 should be taken.
module of a string, assuming all PV Also note in the above table that the current at maximum power point of PV
modules are identical.
array remains the same as that of current of individual PV module, i.e., Ima = Im.
In this step, the calculations for finding out the number of modules to be
connected in series is done using voltage at maximum power point, but similar
calculations can also be done using open circuit voltage of PV modules. Please note
that voltage at maximum power point of a PV module is normally in range of 75%
to 85% of open circuit voltage.
Step 4 Estimating the total power of the series connected PV modules: The
total power of the PV array in series connected PV modules is the sum of the
maximum power of individual PV modules. Thus, if Ns PV modules are connected
in series and maximum power of one PV module is Pm, then the total power output
of the PV array (Pma) would be Ns  Pm. Thus, by connecting PV modules in series,
not only the voltage but the total power of the series connected PV modules also
increases, depending on the number of PV modules connected in series. The PV
array power output can also be calculated from PV array voltage and current at
maximum power point, Vma and Ima. The PV module array power is the product of
Vma and Ima, that is, Pma = Vma  Ima. This can be tabulated (Table 5.3) in following
way:

Table 5.3 Calculation of PV Modules Array

PV module parameter Symbol Value Unit

PV array voltage at maximum power point (note actual PV voltage, this can be Vma = Vm  Ns volt
higher than the required voltage, because we have to take integer value of Vma /Vm)
PV array current at maximum power point Ima volt
Maximum power of single PV module Pm watt
Number of PV modules in series, Ns Ns number
Maximum power of PV module array# Pma = Pm × Ns watt
= Vm × Im × Ns
or Pma = Vma × Ima

#
Because of approximating Ns value to the next higher integer value in Step 3, the value of Vma will be higher than the initial desired
value noted in Step 1.

Example 5.1 Calculate the number of modules to be connected in series to obtain the open circuit
voltage of the array as 40 V and/or maximum power point voltage of 32 V. The
modules available for connection are having the following parameters:
Voc = 20 V, Vm = 16 V, Isc = 4 A and Im = 3 A
94 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Solution Step 1 Note down the voltage requirement of series connected PV modules:

PV module parameter Symbol Value Unit

PV module array open circuit voltage Voca 40 volt
PV module array at maximum power point Vma 32 volt

Step 2 Note down the parameter of a PV module that is to be connected in

series:

PV module parameter Symbol Value Unit

Open circuit voltage of module Voc 20 volt
Short circuit current of PV module Isc 4 ampere
Voltage at maximum power point Vm 16 volt
Current at maximum power point Im 3 ampere
Maximum power of PV module Pm = Vm × Im 48 watt

Step 3 Estimating the number of PV modules to be connected in series:

PV module parameter Symbol Value Unit

Required PV array voltage at maximum Vma 32 volt
power point
Voltage at maximum power point of Vm 16 volt
single PV module
Number of PV modules in series, Ns Ns = (Vma /Vm) (32 /16) = 2 number
Current at maximum power point of Ima = Im 3 ampere
PV array

Figure 5.6 shows two modules connected in series to make array.

Figure 5.6
Two modules connected in series to
make array.
Total power of number of PV modules
connected in series is sum of powers
of individual PV modules, assuming
all modules are identical.
 Chapter 5: Solar PV Module Arrays 95

Step 4 Estimating the total power of the series connected PV modules:

PV module parameter Symbol Value Unit

PV array voltage at Vma 32 volt
maximum power point
PV array current at Ima 3 amperes
maximum power point
Maximum power of Pm 48 watt
single PV module
Number of PV Ns 2 number
modules in series (Ns)
Maximum power of Pma = Pm × Ns 48 × 2 watt
PV module array or Pma = Vma × Ima or 32 × 3
or Pma = Vm × Im × Ns or 16 × 3 × 2 = 96

Example 5.2 Calculate the number of modules to be connected in series to obtain maximum
power point voltage of 70 V. The modules available for connection are having
following parameters.
Voc = 20 V, Vm = 15 V, Isc = 5 A and Im = 3.5 A
Solution Step 1 Note down the voltage requirement of series connected PV modules:
PV module parameter Symbol Value Unit
PV module array open circuit voltage Voca (not given) volt
PV module array at maximum power point Vma 70 volt

Step 2 Note down the parameter of a PV module that is to be connected in

series:
PV module parameter Symbol Value Unit
Open circuit voltage of module Voc 20 volt
Short circuit current of PV module Isc 5 ampere
Voltage at maximum power point Vm 15 volt
Current at maximum power point Im 3.5 ampere
Maximum power of PV module Pm = Vm × Im 52.5 watt

Step 3 Estimating the number of PV modules to be connected in series:

PV module parameter Symbol Value Unit
Required PV array voltage at Vma 70 volt
maximum power point
Voltage at maximum power Vm 15 volt
point of single PV module
Number of PV modules in Ns = (Vma/Vm) 70/15 4.66 modules can
series, Ns = 4.66 not be connected in
≈5 series, we have to
connect 5 modules
Current at maximum power Ima = Im 3.5 ampere
point of PV array

Figure 5.7 shows five identical modules connected in series (a PV module string).
96 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Figure 5.7
Five identical modules connected in
series (a PV module string).

Step 4 Estimating the total power of the series connected PV modules:

PV module parameter Symbol Value Unit
PV array voltage at Vma = Vm × Ns 15  5 = 75 volt
maximum power point
(note here the designed
array voltage, 75 V, is
higher than the required
voltage, 70 V)
PV array current at Ima 15 volt
maximum power point
Maximum power of single Pm 52.5 watt
PV module
Number of PV modules in Ns 5 number
series (Ns)
Maximum power of PV Pma = Pm × Ns 52.5 × 5 watt
module array or Pma = Vma × Ima or 75 × 3.5
or Pma = Vm × Im × Ns or 15 × 3.5 × 5
  = 262.5

Example 5.3 In a PV power plant of 1 MW capacity, a large number of PV modules are

connected in series. In such plants, 1 MW inverter can take input voltage in range of
600 V to 800 V. Design the number of PV modules to be connected in a single
series (PV module string) to obtain voltage at maximum power point of 700 V.
Also, estimate the peak power that will be supplied by one such PV module string.
The parameters of PV modules to be used are:
Voc = 36 V, Vm = 30 V, Isc = 8.2 A and Im = 7.4 A.
Solution Step 1 Note down the voltage requirement of series connected PV modules:
PV module parameter Symbol Value Unit
PV module array open circuit voltage Voca (not given) volt
PV module array at maximum power point Vma 700 volt
Step 2 Note down the parameter of a PV module that is to be connected in
series:
PV module parameter Symbol Value Unit
Open circuit voltage of module Voc 36.00 volt
Short circuit current of PV module Isc 8.2 ampere
Voltage at maximum power point Vm 30.00 volt
Current at maximum power point Im 7.4 ampere
Maximum power of PV module Pm = Vm × Im 30 × 7.4 = 222 watt
 Chapter 5: Solar PV Module Arrays 97

Step 3 Estimating the number of PV modules to be connected in series:

PV module parameter Symbol Value Unit
Required PV array voltage at Vma 700 volt
maximum power point
Voltage at maximum power Vm 30 volt
point of single PV module
Number of PV modules in Ns = Vma/Vm 700 ÷ 30 23.33 modules can
series (Ns) = 23.333 not be connected
≈ 24 in series, therefore,
we have to connect
24 modules
Current at maximum power Ima = Im 7.4 ampere
point of PV array

Figure 5.8 shows 24 modules connected in series (a PV module string).

Figure 5.8
24 modules connected in series
(a PV module string).

Step 4 Estimating the total power of the series connected PV modules:

PV module parameter Symbol Value Unit

PV array voltage at Vma = Vm × Ns 30 × 24 = 720 volt
maximum power point
(note here the designed
array voltage, 75 V, is
higher than the required
voltage, 70 V)
PV array current at Ima 7.4 volt
maximum power point
Maximum power of Pm 222 watt
single PV module
Number of PV modules Ns 24 number
in series, Ns
Maximum power of PV Pma = Pm × Ns 222 × 24 watt
module array or Pma = Vma × Ima or 720 × 7.4
or Pma = Vm × Im × Ns or 30 × 7.4 × 24
  = 5328

Worksheet 5.2: In a PV power plant of 1 MW capacity, a large number of PV modules are connected
in series. In such plants, 1 MW inverter can take input voltage in range of 400 V to 500 V. Design the
number of PV modules to be connected in a single series (PV module string) to obtain voltage at maximum
power point of 450 V. Also, estimate the peak power that will be supplied by one such PV module string.
The parameters of PV modules to be used are: Voc = 45 V, Vm = 35 V, Isc = 8.2 A and Im = 7.8 A.
98 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Step 1 Note down the voltage requirement of series connected PV modules:

PV module parameter Symbol Value Unit
PV module array open circuit voltage Voca (not given) volt
PV module array at maximum power point Vma 450 volt

Step 2 Note down the parameter of a PV module that is to be connected in series:

PV module parameter Symbol Value Unit
Open circuit voltage of module Voc volt
Short circuit current of PV module Isc ampere
Voltage at maximum power point Vm volt
Current at maximum power point Im ampere
Maximum power of PV module Pm = Vm × Im _____ × _____ = _____ watt

Step 3 Estimating the number of PV modules to be connected in series:

PV module parameter Symbol Value Unit
Required PV array voltage at maximum power point Vma volt
Voltage at maximum power point of single PV Vm volt
module
Number of PV modules in series (Ns) Ns = Vma/Vm ____ ÷ ____ 23.33 modules cannot be
= ______ connected in series, we have
≈ ______ to connect 24 modules
Current at maximum power point of PV array Ima = Im ampere

Step 4 Estimating the total power of the series connected PV modules:

PV module parameter Symbol Value Unit
PV array voltage at maximum power point (note Vma = Vm × Ns ______ × _______ = ______ volt
here the designed array voltage, 75 V, is higher
than the required voltage, 70 V)
PV array current at maximum power point Ima volt
Maximum power of single PV module Pm watt
Number of PV modules in series (Ns) Ns number
Maximum power of PV module array Pma = Pm × Ns _____ × _____ watt
or Pma = Vma × Ima or _____ × _____
or Pma = Vm × Im × Ns or _____ × _____ × _____
  = _____

Figure 5.9
____ modules connected in series
(a PV module string).
 Chapter 5: Solar PV Module Arrays 99

5.1.2 Maximum power or the peak power output of a PV module (under STC) is the
Mismatch in Voltage in product of current at maximum power point (Im) and voltage at maximum power
point (Vm). When PV modules are not connected with each other, the total peak
Series Connected PV power produced by PV modules is the sum of the total peak power produced
Modules by individual modules. An example of total power produced by three individual
PV modules is given in Table 5.4.

Table 5.4 Total Power Produced by PV Modules When Working Independently

Vm (V) Im (A) Pm (watt) = Vm × Im

Module 1 17 5.1 86.7
Module 2 16.5 5.1 84.15
Module 3 16.3 5.1 83.13
Total wattage produced by three modules when not connected with each other 253.98 watt

Now, let us take the case when the three PV modules mentioned in Table 5.4 are
connected in series. In series connection, only voltage gets added but current in
series combination remains the same, provided all the modules are with identical
current values. For example, in Table 5.4, all the PV modules have Im of 5.1 A
each. Therefore, the current, when three modules are connected in series will be
5.1 A. An example of calculation of Pm of three series connected PV modules is
given in Table 5.5. Compare the total power output of these three series connected
PV modules (Table 5.5) with the power output of three individual PV modules
(Table 5.4). One can notice that the difference in Vm of three series connected PV
modules does not affect the total power output of series connected PV modules.
But the differences in current of series connected PV modules do affect the power
Mismatch in voltages of series output of series connected PV modules (as discussed in Section 5.1.3).
connected PV modules is not an The difference in the voltages of series connected PV modules does not affect
issue, mismatch in currents is.
the total power generating capacity of the combination.

Table 5.5 Calculation of Pm of Three PV Modules Connected in Series with Identical Current

Vm (V) Im (A) Pm (watt)

Module 1 170. 5.1 86.70
Module 2 16.5 5.1 84.15
Module 3 16.3 5.1 83.13
Total voltage of series combination Total current of series combination Total power of series combination
49.8 5.1 49.8 × 5.1 = 253.98 watt
Total wattage produced by three PV modules when connected with each other in series.

5.1.3 In series connection, only voltage gets added but current remains the same, provided
Mismatch in Current in all the modules are with identical current values. If the current producing capacity
of the PV modules is not same, then the current flowing in the series connected
Series Connected PV modules will be equal to the current of the module with the lowest current producing
Modules capacity. Thus, the lowest current producing module determines the current in series
connected modules. For examples, if there are three modules having Im of 5.1 A,
4.9 A and 5.0 A, then the current of the series combination of these modules will
be 4.9 A (which is smallest of three currents). Due to this mismatch in current,
the power generation from the series combination of three modules will be less
than the case when the three modules are working independently. An example of
mismatch in series connected PV modules and its effect of total power generation
is given in Table 5.6. It can be noticed that the total power generation capacity of
100 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

three individual modules is 249.05 watt but when connected in series, the power
generation capacity of combination is reduced to 244.02 watt. Due to such power
generation losses, it is advised that PV modules with difference in Im should not
be connected in series.
PV modules with difference in Im should not be connected in series. It results
in loss of power output.

Table 5.6 Total Power Produced by PV Modules When They are Connected with Each Other in Series (STC Conditions)

Vm (V) Im (A) Pm (watt)

Module 1 170. 5.1000 86.70
Module 2 16.5 4.9000 80.85
Module 3 16.3 5.0000 81.50
Total power of modules when not 249.05 watt
connected in series
Total voltage of series combination Total current of series combination Total power of series combination
49.8 4.9000 49.8 × 4.9 = 244.02 watt
Total wattage produced by three PV modules when connected with each other in series 244.02 watt

5.2 When solar PV system power requirement is higher than the available single module
power, then the solar PV modules are connected in series or parallel. A series
Connection of Modules in connection of PV modules is discussed in Section 5.1. Sometimes, instead of series
Parallel Combination connection of PV modules, a parallel connection is done to increase the power
output. In parallel combination of PV modules, the voltage of the combination
remain the same as that of individual module voltage (provided all modules have
identical voltage) where as the current of the parallel combination is the sum of
currents of all PV modules. The parallel configuration is achieved by connecting
same polarity terminals together. In this way, the positive terminal of one module
is connected to the positive terminal of the other module and similarly, negative
terminal of one module is connected to the negative terminal of other PV module.
The parallel combination of the PV modules is shown in Figure 5.10.

Figure 5.10
Two modules in parallel combination.

As shown in Figure 5.10, two modules are connected in parallel configuration by

connecting their same polarity terminals to each other (positive terminal to positive
and negative terminal to negative). In the parallel combination, individual currents
of each module gets added up. Suppose, the short circuit current of two PV modules
is Isc1 and Isc2, then the total current of parallel connection will be = Isc1 + Isc2. As
the number of modules is added, the current keeps on adding but voltage remains
the same. An example of parallel combination of two PV modules, each having 2 A
The PV modules are connected in
parallel in order to obtain higher
current is given in Table 5.7. The above description is given for short circuit current,
currents in PV systems. Module but it is applicable for any other current component of PV modules. Thus, if current
currents in parallel combination get at maximum power point of two PV modules is Im1 and Im2, then the total current
added up.
at maximum power point of parallel connection will be Im1 + Im2.
 Chapter 5: Solar PV Module Arrays 101

In parallel combination of PV modules, currents get added while the voltage of

combination remains the same as that of a single PV module.

Table 5.7 An Example of Summation of Currents when PV Modules Connected in

The PV modules with different wattages Parallel
should not be connected together in
series or parallel combination. Short circuit current of module 1 Isc1 2 A

Note: Voltage of combination remains Short circuit current of module 2 Isc2 2 A

same as that of single module. Short circuit current of modules connected in series Isc Isc1 + Isc2 = 2 + 2 = 4 A

Example 5.4 What will be the current of three modules connected in parallel as shown in
Figure 5.11.

Figure 5.11
Three modules in parallel connection.

Solution In Figure 5.11, positive terminals of all modules are connected together and negative
terminals of all modules are connected together. It indicates that the PV modules
are connected in parallel configuration.
It is given that the current produced by all PV modules is 2 A. Now, in parallel
combination, the total current is the sum of current of individual PV modules.
Therefore, the total current of the combination will be
= Imodule 1 + Imodule 2 + Imodule 3
= 2 + 2 + 2 = 6 A.

Worksheet 5.3: Find out the total current at maximum power point, Im, of parallel combination of
three PV modules. Current at maximum power point of individual modules is given in Table 5.8.

Table 5.8 Current at Maximum Power Point

Current at maximum power point of module 1 Im1 7.8 A

Current at maximum power point of module 2 Im2 7.7 A
Current at maximum power point of module 3 Im3 7.9 A
Current at maximum power point of parallel combination of PV modules Im Isc1 + Isc2 + Isc3 = ____ + ____ + ____ = ____ A

5.2.1 The Pm of a PV module (under STC) is the product of current at maximum power
Power Generated by point (Im) and voltage at maximum power point (Vm). When PV modules are not
connected with each other, the total peak power produced by the PV modules is
Parallel Connected PV the sum of the peak power produced by individual modules. An example of total
Modules power produced by three individual PV modules (having same Vm but different Im)
is given in Table 5.9. The total power produced by three individual PV modules
is 255 watt. When these modules are connected in parallel, the Vm of the parallel
combination is same as Vm of individual PV modules which is 17 V (from
Table 5.9). Now, the total Im of the parallel combination will be the sum of Im
of each PV modules, which is 15 A (from Table 5.9). The total power produced
by the parallel combination of PV modules is 255 watt which is same as power
produced by individual modules. It indicates that while making parallel connection,
the voltages of modules should be same and the difference in current is acceptable.
102 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Table 5.9 Total Power Produced by Three Individual PV Modules and by Parallel Combination of Same PV Modules
(STC Conditions)

Vm (V) Im (A) Pm (watt) = Vm × Im

Module 1 17 5.1 86.7
Module 2 17 4.9 83.3
Module 3 17 5.0 85.0
Total power of modules when not 255.0 watt
connected with each other
Total voltage of parallel combination Total current of parallel combination Total power of series combination
17 15 17 × 15 = 255.0 watt
Total wattage produced by three PV modules when connected with each other in parallel 255.0 watt

Total power of PV modules connected in parallel is the sum of powers of individual PV modules, assuming all modules are identical.

5.2.2 When PV modules are connected in parallel, the current of individual PV module
Estimating the Number gets added while the voltage of the parallel combination remains the same. Therefore,
the main purpose of parallel combination of PV modules is to increase the current
of PV Modules to be of combination. In a PV array, either individual PV modules can be connected in
Connected in Parallel and parallel or PV module strings (series connected PV modules) can be connected in
Their Total Power parallel. In this section, we will learn to calculate the number of PV modules or
PV module strings to be connected in parallel if the requirement of total current
of PV system is known. Also, we should be able to estimate the total power that
the parallel connected PV modules will be generating. Here it is assumed that all
PV modules are identical, having identical parameters like Voc, Vm, Isc and Im. This
exercise can be done in the following steps:
Step 1 Note down the current requirement of parallel connected PV modules
or PV array: Since the idea is to connect PV modules or PV module strings in
parallel (to form a PV module array) to increase the current of PV array. How much
current is required from PV module array should be noted as follows:
PV module parameter Symbol Value Unit
Short circuit current of PV module array Isca ampere
Current at maximum power point of PV Ima ampere
module array

Step 2 Note down the parameter of a PV module or PV module string that is

to be connected in parallel: Since in operation, it is expected that a PV module
or a PV module string operates under maximum power point condition, therefore,
current and voltage at maximum power point, that is, Vm and Im of available PV
module or PV module strings must be noted. Other PV module informations like
Voc, Isc and Pm can also be noted in the following table:
PV module or PV module string parameter Symbol Value Unit
Open circuit voltage of module or string Voc volt
Short circuit current of PV module or string Isc ampere
Voltage at maximum power point or string Vm volt
Current at maximum power point or string Im ampere
Maximum power of PV module or string Pm = Vm × Im watt

Step 3 Estimating the number of PV modules or strings to be connected in

parallel: In order to find out the number of PV modules to be connected in
parallel, total array current (Ima) is divided by the current of individual modules or
 Chapter 5: Solar PV Module Arrays 103

module string (Ima). Since in real time, PV modules are supposed to work under
maximum power point condition, the ratio of Ima to Im (PV array current to module
current at maximum power point) should be taken as follows:
PV module parameter Symbol Value Unit
Required PV array current at maximum power Ima ampere
point
Current at maximum power point of single PV Im ampere
module or PV module string
Number of PV modules to be connected in Np = Ima/Im number
parallel, Np
Voltage at maximum power point of PV array Vma = Vm volts
If the ratio of Ima to Im is not an integer, then the next integer value should be
taken. For instance, if the ratio is 4.7, then we know that number of modules in
parallel cannot be 4.7, therefore, it can be either 4 or 5. Hence, in this case, the next
integer number, that is 5 should be taken. It means that the number of modules or
PV strings to be connected in parallel is 5.
The number of PV modules connected
in parallel is obtained by dividing
In parallel connection, the voltage of the PV array, remains the same as that of
the desired current from the parallel voltage of individual PV module or PV module string. Therefore, note here, in the
combination with current of individual above table that the voltage at maximum power point of PV array remains same as
PV module.
that of voltage of individual PV module or module string, i.e. Vma = Vm.
In this step, the calculations for finding out the number of modules to be
connected in parallel is done using current at maximum power point, but similar
calculations can also be done using short circuit current of PV modules. Please note
that module current at maximum power point is normally in range of 85% to 95%
of current of short circuit point.
Step 4 Estimating the total power of the series connected PV modules: The
total power of the PV array in parallel connected PV modules is the sum of the
maximum power of individual PV modules or the total power of the PV array
in parallel connected PV module strings is the sum of the maximum power of
individual PV modules strings. Thus, if Np PV modules or strings are connected
in parallel and maximum power of one PV module or string is Pm, then the total
power output of the PV array is Pma = Np  Pm. The PV array power output can
also be calculated from PV array voltage and current at maximum power point, that
is, Vma and Ima. The PV module array power is the product of Vma and Ima, that is,
Pma = Vma  Ima. This can be tabulated in the following way:
PV module parameter Symbol Value Unit
PV array voltage at maximum power Vma = Vm volt
point
PV array current at maximum power Ima = Np × Im volt
point#
Maximum power of single PV module Pm watt
Number of PV modules to be Np number
connected in parallel (Np)
Maximum power of PV module array Pma = Pm × Np watt
or = Vm × Im × Np
or = Vma × Ima
#
Because of approximating Np value to the next higher integer value in Step 3, the value of Ima
will be higher than the initial desired value noted in Step 1.
104 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Example 5.5 Estimate the number of SPV modules to be connected in parallel to achieve the
current at peak power point of 42 A. The system voltage requirement is 16 volts.
The modules to be connected are having parameters Vm = 16 V, Im = 7 A,
Voc = 20 V, Isc = 8.5 A.
Solution Step 1 Note down the current requirement of parallel connected PV modules
or PV array:
PV module parameter Symbol Value Unit
Short circuit current of PV module array Isca (not given) ampere
Current at maximum power point of PV module Ima 42 ampere
array

Step 2 Note down the parameter of a PV module or PV module string that is

to be connected in parallel:
PV module or PV module string parameter Symbol Value Unit
Open circuit voltage of module or string Voc 20 volt
Short circuit current of PV module or string Isc 8.5 ampere
Voltage at maximum power point or string Vm 16 volt
Current at maximum power point or string Im 7 ampere
Maximum power of PV module or string Pm = Vm × Im = 7 × 16 watt
= 112

Step 3 Estimating the number of PV modules or strings to be connected in

parallel:
PV module parameter Symbol Value Unit
Required PV array current at maximum power Ima 42 ampere
point
Current at maximum power point of single PV Im 7 ampere
module or PV module string
Number of PV modules to be connected in Np = Ima/Im = 42 ÷ 7 number
parallel (Np) =6
Voltage at maximum power point of PV array Vma = Vm 16 volts

Step 4 Estimating the total power of the series connected PV modules:

PV module parameter Symbol Value Unit
PV array voltage at maximum Vma = Vm 16 volt
power point
PV array current at maximum Ima = Np × Im = 6 × 7 = 42 volt
power point
Maximum power of single Pm 112 watt
PV module
Number of PV modules to be Np 6 number
connected in parallel (Np)
Maximum power of PV Pma = Pm × Np = 112 × 6 watt
module array or = Vm × Im × Np = 16 × 7 × 6
or = Vma × Ima = 16 × 42
= 672
 Chapter 5: Solar PV Module Arrays 105

Figure 5.12
Six modules connected in parallel
combination.

Worksheet 5.4: Find out the number of modules to be connected in parallel and series combination
for voltage and current requirement of 40 V and 60 A respectively (at maximum power point). The modules
available for this power plant are with parameters Vm = 40 V, Im = 6 A. Also, calculate the total power
rating of the power plant.

Step 1 Note down the current requirement of parallel connected PV modules or PV array:

PV module parameter Symbol Value Unit

Short circuit current of PV module array Isca (not given) ampere
Current at maximum power point of PV module array Ima 60 ampere

Step 2 Note down the parameter of a PV module or PV module string that is to be connected in parallel:
PV module or PV module string parameter Symbol Value Unit
Open circuit voltage of module or string Voc volt
Short circuit current of PV module or string Isc ampere
Voltage at maximum power point or string Vm volt
Current at maximum power point or string Im ampere
Maximum power of PV module or string Pm = Vm × Im ____ × ____ = ____ watt

Step 3 Estimating the number of PV modules or strings to be connected in parallel:

PV module parameter Symbol Value Unit
Required PV array current at maximum power point Ima ampere
Current at maximum power point of single PV module Im ampere
or PV module string
Number of PV modules to be connected in parallel Np = Ima/Im _____ ÷ _____ number
(Np) = ______ ≈ ______
Voltage at maximum power point of PV array Vma = Vm 35 volts

Step 4 Estimating the total power of the series connected PV modules:

PV module parameter Symbol Value Unit

PV array voltage at maximum power point Vma = Vm volt
PV array current at maximum power point Ima = Np × Im ____ × ____ = ____ volt
Maximum power of single PV module Pm watt
Number of PV modules to be connected in Np number
parallel (Np)
Maximum power of PV module array Pma = Pm × Np ____ × ____ watt
or = Vm × Im × Np ____ × ____ × ____
or = Vma × Ima ____ × ____
= ____
106 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Figure 5.13
_____ modules connected in parallel
combination (to be drawn by the
readers).

Example 5.6 Estimate the number of modules required to fulfill the maximum power point current
of 96 A, with maximum voltage of 35 V. The modules available are having the
following parameters:
Voc = 40 V, Vm = 36 V, Isc = 8.5 A, Im = 7.5 A
Also, find out the total power of the plant designed.
Solution Step 1 Note down the current requirement of parallel connected PV modules
or PV array:
PV module parameter Symbol Value Unit
Short circuit current of PV module array Isca (not given) ampere
Current at maximum power point of PV Ima 96 ampere
module array

Step 2 Note down the parameter of a PV module or PV module string that is

to be connected in parallel:
PV module or PV module string parameter Symbol Value Unit
Open circuit voltage of module or string Voc 40 volt
Short circuit current of PV module or string Isc 8.5 ampere
Voltage at maximum power point or string Vm 36 volt
Current at maximum power point or string Im 7.5 ampere
Maximum power of PV module or string Pm = Vm × Im 36 × 7.5 watt
= 270

Step 3 Estimating the number of PV modules or strings to be connected in

parallel:
PV module parameter Symbol Value Unit
Required PV array current at maximum Ima 95 ampere
power point
Current at maximum power point of single Im 7.5 ampere
PV module or PV module string
Number of PV modules to be connected Np = Ima/Im 96 ÷ 7.5 number
in parallel (Np) = 12.8
≈ 13
Voltage at maximum power point of PV Vma = Vm 36 volts
array
 Chapter 5: Solar PV Module Arrays 107

Step 4 Estimating the total power of the series connected PV modules:

PV module parameter Symbol Value Unit

PV array voltage at Vma = Vm 36 volt
maximum power point
PV array current at Ima = Np × Im 13 × 7.5 = 97.5 volt
maximum power point
Maximum power of Pm 270 watt
single PV module
Number of PV modules Np 13 number
to be connected in parallel
(Np)
Maximum power of PV Pma = Pm × Np 270 × 13 watt
module array or = Vm × Im × Np 36 × 7.5 × 13
or = Vma × Ima 36 × 97.5
  = 3510

Worksheet 5.5: Estimate the number of SPV modules to be connected in parallel to achieve the current
requirement of 100 A. The system voltage requirement is 35 Volts. The modules to be connected are having
parameters Vm = 36 V, Im = 8 A, Voc = 45 V, Isc = 8.75 A.

Step 1 Note down the current requirement of parallel connected PV modules or PV array:

PV module parameter Symbol Value Unit

Short circuit current of PV module array Isca (not given) ampere
Current at maximum power point of PV module array Ima 100 ampere

Step 2 Note down the parameter of a PV module or PV module string that is to be connected in parallel:
PV module or PV module string parameter Symbol Value Unit
Open circuit voltage of module or string Voc volt
Short circuit current of PV module or string Isc ampere
Voltage at maximum power point or string Vm volt
Current at maximum power point or string Im ampere
Maximum power of PV module or string Pm = Vm × Im ____ × ____ = ______ watt

Step 3 Estimating the number of PV modules or strings to be connected in parallel:

PV module parameter Symbol Value Unit

Required PV array current at maximum power point Ima 100 ampere
Current at maximum power point of single PV module Im 8 ampere
or PV module string
Number of PV modules to be connected in parallel (Np) Np = Ima /Im _____ ÷ _____ = ______ number
≈ ______
Voltage at maximum power point of PV array Vma = Vm volts
108 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Step 4 Estimating the total power of the series connected PV modules:

PV module parameter Symbol Value Unit

PV array voltage at maximum power point Vma = Vm volt
PV array current at maximum power point Ima = Np × Im ____ × ____ = ____ volt
Maximum power of single PV module Pm watt
Number of PV modules to be connected in parallel Np number
(Np)
Maximum power of PV module array Pma = Pm × Np ____ × ____ watt
or = Vm × Im × Np ____ × ____ × ____
____ × ____
or = Vma × Ima
= ____

Figure 5.14
____ modules connected in parallel
combination (to be drawn by the
readers).

5.2.3 It has been mentioned that the voltage of parallel combination of PV modules is
Mismatch in Module equal to the voltage of a single module, if the module voltages are identical. If there
is difference in PV module voltages, then the voltage of the parallel combination is
Voltages Connected in determined by the PV module with lowest voltage. Normally, the effect of difference
Parallel in modules voltages in parallel combination is not as severe as the difference in
module currents in series combination. In general, as a practice, care should be
taken to avoid series or parallel connection of the PV modules of different power
ratings (means different current and voltage rating). Or, if, there is need to connect
Mismatch in currents of PV modules PV modules of different power ratings together, efforts should be made to put PV
connected in parallel is not an issue, modules of same current rating in series combination and PV modules of same
mismatch in voltages is. voltage ratings in parallel combination.

5.3 When the PV power requirement is more than few hundred watts, the PV modules
needs to be connected in both series and in parallel combination. Also, when we need
Connection of Modules in to generate a very large amount of power, like in solar PV megawatt scale power
Series and Parallel plants, then the PV modules are connected in both series and parallel configuration
(Mixed Combination) to increase the required current as well as voltage. Just to remind you that the series
connection of PV module increases the voltage levels while the parallel connection
of PV modules increases the current levels. Normally, in big PV power plants,
many PV modules are connected in series. The series connected PV modules may
be referred as PV module ‘string’. In a PV system, the number of PV modules is
first connected in series (string) as per the requirement of system voltage, and then
many PV module strings are connected together in parallel. An example of series
and parallel combination of four PV modules is shown in Figure 5.15.
 Chapter 5: Solar PV Module Arrays 109

Figure 5.15
Series and parallel combination of PV
modules.

In this example, four identical PV modules (Module 1, Module 2, Module 3 and

Module 4) with open circuit voltage of Voc and short circuit current of Isc are used.
In Figure 5.15, the connection of four identical PV modules is shown, each
PV module having short circuit current of Isc and open circuit voltage of Voc. A
close observation of the Figure 5.15 will show that two PV modules are connected
in series (a PV module string), and two such strings are connected in parallel. In
series connection of PV modules, the voltage gets added while current remains
the same and in parallel connection of PV modules, the current gets added and
110 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

voltage remains the same. In this case, Module 1 and Module 2 (in Figure 5.15)
are connected in series, let us call it string 1. Similarly, Module 3 and Module 4
are also connected in series, and let us call it string 2. Since all the PV modules
are identical, the open circuit voltage of string 1 (Voc1) and short circuit current of
PV module string 1 (Isc1) will be 2 × Voc and Isc respectively (refer to Table 5.10).
Similarly, the the open circuit voltage of PV module string 2 will be 2 × Voc while
the short circuit current will be Isc.

Table 5.10 Example of Summation of Currents and Voltages in Series and Parallel Combination of PV Modules (Voltage
Adds up in Series Connection and Current Adds up in Parallel Connection)

Open circuit voltage of PV modules Voc

Short circuit current of PV modules Isc
Module 1 and Module 2 are connected in series (string 1)
(voltage gets added up but current remains same)
Open circuit voltage of PV module string 1, Voc1 Voc1 = Voc + Voc = 2Voc
Short circuit current of PV module string 1, Isc1 Isc1 = Isc
Module 3 and Module 4 are connected in series (string 2)
Open circuit voltage of PV module string 2, Voc2 Voc2 = Voc + Voc = 2Voc
Short circuit current of PV module string 2, Isc2 Isc2 = Isc
PV module string 1 and string 2 are connected in parallel (voltage remains the same but current
gets added), the combination is called array
Open circuit voltage of PV module array (Vocr) Vocr = Voc1 = Voc2 = 2Voc
Short circuit current of PV module array (Iscr) Iscr = Isc1 + Isc2 = Isc + Isc = 2Isc

Now, the PV module string 1 and string 2 are connected in parallel (this combination
of series and parallel PV modules is called PV module array). In parallel combination,
voltage remains the same but currents get added. As given in Table 5.10, since the
open circuit voltage of the both the PV strings is same (Voc1 = 2Voc, and Voc2 = 2Voc),
the open circuit voltage of the PV module array, Vocr = Voc1 = Voc2 = 2Voc. The short
circuit current of string 1 is Isc1 = Isc and that of string 2 is Isc2 = Isc. Therefore the
In high power PV systems, PV
modules are connected in series and short circuit current of PV module array, Iscr, wherein two strings are connected in
many such series are connected in parallel is Isc1 + Isc2 = Isc + Isc = 2Isc. In this case of PV module array, the array
parallel. open circuit voltage will be 2Voc and the array short circuit current will be 2Isc.
In the same way, current and voltage of any combination of series and parallel
In a PV system, voltage increases due
connected PV modules can be obtained. In practice, PV modules do not operate at
to series connection, current increases
due to parallel connection, and power open circuit and short circuit conditions, but they operate under maximum power
increases in both series and parallel point condition. Therefore, for calculations, current at maximum power point (Im)
connection. and voltage at maximum power point (Vm) should be taken for calculations.

5.3.1 The objective of making series and parallel combination of PV modules, to form
Estimation Number of PV array, is to increase the current as well as the voltage of combination in order
to get higher power. In PV module array, modules are connected in series (to form
Modules to be Connected module string) to get higher voltages and modules or module strings are connected
in Series and Parallel and in parallel to get higher currents. In both series and parallel combination, the power
their Total Power output of the combination increases.
PV array formation is required as soon as PV power requirement is higher than
the individual power output. Individual PV modules are available in few watt to
few hundred watt power range. Nowadays, PV arrays are installed for household
 Chapter 5: Solar PV Module Arrays 111

application wherein the power requirement ranges from few hundred watts to few
kilowatts (kW). The PV power plants are installed with power range from few
hundred kW to several megawatt (MW). In this section, we will learn to calculate
the number of PV modules to be connected in series, and the number of PV modules
to be connected in parallel in order to get desired power output of PV module array.
Here, it is assumed that all PV modules are identical, having identical parameters
like Voc, Vm, Isc and Im. The estimation of number of series and parallel connected
PV modules can be done in the following steps:

Step 1 Note down the voltage, current and power requirement of PV module
array: In PV module array, the idea is to connect PV modules in series and in
parallel to increase both voltage and current in PV module array, and to increase
power. The desired power of array, Pma, should be noted. If the desired current of
array (Ima) and desired voltage of array (Vma) are mentioned, then note it down.
Else, if only one of the parameter (current or voltage) is given then other parameter
can be estimated using Pma = Ima × Vma relationship. All three parameters; power,
voltage and current are assumed at maximum power point condition.

PV module parameter Symbol Value Unit

PV array power requirement (peak power Pma watt
or maximum power point)
PV module array open circuit voltage at Vma or Pma /Ima volt
peak power
PV module array current at peak power Ima or Pma /Vma ampere

Step 2 Note down the parameter of a PV module that is to be connected in

PV array: Since in operation, it is expected that a PV module operates under
maximum power point condition, therefore, current and voltage at maximum power
point, that is, Vm and Im of a PV module to be connected in PV array, must be
noted. Other PV modules information like Voc, Isc and Pm can also be noted in the
following Table:

PV module parameter Symbol Value Unit

Open circuit voltage of module Voc volt
Short circuit current of PV module Isc ampere
Voltage at maximum power point Vm volt
Current at maximum power point Im ampere
Maximum power of PV module Pm = Vm × Im watt

Step 3 Estimating the number of PV modules to be connected in series and

parallel: In order to find out the number of PV modules to be connected in series
(voltage addition), total array voltage is divided by the voltage of individual modules.
And, in order to find out the number of PV modules or PV module strings to be
connected in parallel (current addition), PV array current should be divided by the
current of individual PV modules or module string. All the parameters are to be
taken under maximum power point condition because PV array is assumed to work
under maximum power point condition.
112 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

PV module parameter Symbol Value Unit

Required PV array voltage at maximum Vma volt
power point
Voltage at maximum power point of single Vm volt
PV module or PV string
Number of PV modules in series (Ns) Ns = Vma /Vm number
Current at maximum power point of PV array Ima ampere
Current at maximum power point of PV Im ampere
module or PV string
Number of PV modules in series (Np) Np = Ima /Im number

The value of Ns and Np should be an integer. If the calculated ratio is not an integer,
then the next higher integer value should be chosen. Thus, if Ns is 3.7, then next
higher integer value, that is, 4 should be taken. It means that four PV modules
should be connected in series. If Np is 6.7, then the next higher integer value, that
is, 7 should be taken. It means that the 7 PV modules or PV module strings should
be connected in parallel. In this case, the PV module array will satisfy both current
and voltage requirements.
In this step, the calculation for obtaining the number of PV modules to be
connected in series is done using voltage at maximum power point but the same
calculation can be done using open circuit voltage. Also, the calculation for obtaining
the number of modules or module strings to be connected in parallel is done using
current at maximum power point, but similar calculation can also be done using
short circuit current of PV modules. Please note that voltage at maximum power
point of a PV module is normally in the range of 75% to 85% in open circuit. And,
module current at maximum power point is normally in the range of 85% to 95%
of current at short circuit point.

Step 4 Estimating the total power of the series PV module array: Normally,
before designing the number of PV modules in series and parallel, we should know
the total PV array power for which we need to do the design. Therefore, this step
is to be done in order to cross check the design. The total power of the PV array,
wherein PV modules are connected in series as well as in parallel, is the sum of
power of all PV modules connected in PV array. In series connection, voltage and
power of modules gets added up, and in parallel connection, current and power of
PV modules gets added up. Thus, if Ns PV modules are connected in series and
Np such series are connected in parallel, then the total number of PV modules
connected in PV arrays is Ns × Np. Now, if maximum power of one PV module is
Pm, then the total power output of the PV array (Pma) would be Ns × Np × Pm. In
this process, it is assumed that all PV modules connected in series and in parallel
are identical. The PV array power output can also be calculated from PV array
voltage and current at maximum power point, that is Vma and Ima. The PV module
array power is the product of Vma and Ima and
Pma = Vma × Ima
 Chapter 5: Solar PV Module Arrays 113

This can be tabulated in the following way:

PV module parameter Symbol Value Unit

Number of PV modules in Ns number
series (Ns)
Number of PV modules or Np number
module strings in parallel (Np)
New value of PV array voltage Vma = Vm × Ns volt
at maximum power point#
New value of PV array current Ima = Im × Np volt
at maximum power point#
Maximum power of single PV Pm = Vm × Im watt
Design of large power PV plants can module
be done by designing the appropriate
numbers of PV modules in series, and Maximum power of PV module Pma = Pm × Ns × Np watt
appropriate number of PV modules array# = Vm × Im × Ns × Np
series in parallel to fulfill desired power
requirements. or Pma = Vma × Ima
#
Note that because of converting Ns and Np ratio to next higher integer value, the new calculated
value of Ima and Vma in above table will be higher than the desired value of Ima and Vma as
noted in Step 1. As a result of this, the new calculated PV array power will also be higher than
the desired value of power for which design is done.

Example 5.7 Estimate the number of PV modules to be connected together in order to design a
solar PV system for power generation with following requirements:
Power = 10 kW, Voltage at peak power = 200 V, Current at peak power = 50 A,
The PV modules available for this plant are having the following parameters:
Vm = 35 V, Im = 8.5 A. Recalculate the numbers. After calculation of number
of PV modules, estimate the actual peak power of the system.
Solution Since the peak voltage and current requirement of the PV system is higher than the
peak voltage and current of individual PV modules, it is required to connect the PV
modules in series to get desired voltage (higher than individual module voltage) and
connect the PV modules strings in parallel to get the desired current (higher than
individual module current). The following procedure can be adopted to estimate the
number of PV modules to be connected in series and parallel.

Step 1 Note down the voltage, current and power requirement of PV module
array:

PV module parameter Symbol Value Unit

PV array power requirement (peak Pma 10,000 watt
power or maximum power point)
PV module array open circuit Vma or = Pma/Ima =10000 ÷ 50 volt
voltage at peak power (it is given = 200
here but can also be calculated if
Ima is known)
PV module array current at peak Ima or = Pma/Vma = 10000 ÷ 200 ampere
power (it is given here but can also = 50
be calculated if Vma is known)
114 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Step 2 Note down the parameter of a PV module that is to be connected in

PV array:
PV module parameter Symbol Value Unit
Open circuit voltage of module Voc (not given) volt
Short circuit current of PV module Isc (not given) ampere
Voltage at maximum power point Vm 35 volt
Current at maximum power point Im 8.5 ampere
Maximum power of PV module Pm = Vm × Im 35 × 8.5 = 297.5 watt

Step 3 Estimating the number of PV modules to be connected in series and parallel:

PV module parameter Symbol Value Unit
Required PV array voltage at maximum Vma 200 volt
power point
Voltage at maximum power point of Vm 35 volt
single PV module or PV string
Number of PV modules in series (Ns) Ns = Vma/Vm = 200 ÷ 35 number
= 5.71
≈6
Current at maximum power point of PV Ima 50 ampere
array
Current at maximum power point of PV Im 8.5 ampere
module or PV string
Number of PV modules in series (Np) Np = Ima /Im = 50 ÷ 8.5 number
= 5.88
≈6
Figure 5.16 shows six modules in series and six such PV modules strings in parallel.
Step 4 Estimating the total power of the series PV module array:

PV module parameter Symbol Value Unit

Number of PV mod- Ns 6 number
ules in series (Ns)
Number of PV mod- Np 6 number
ules or module strings
in parallel (Np)
New value of PV Vma = Vm × Ns = 35 × 6 volt
array voltage at max- = 210
imum power point
New value of PV Ima = Im × Np = 8.5 × 6 ampere
array current at = 51
maximum power
point
Maximum power of Pm = Vm × Im = 35  ×  8.5 watt
single PV module = 297.5
Maximum power of Pma = Pm  ×  Ns  ×  Np = 297.5  ×  6  ×  6 watt
PV module array or = Vm  ×  Im  ×  Ns  ×  Np or = 35  ×  8.5  ×  6  ×  6
or Pma = Vma  ×  Ima or = 210  ×  51
= 10710
 Chapter 5: Solar PV Module Arrays 115

Figure 5.16
Six modules in series and six such
PV modules strings in parallel.
In MW size PV power plants, many
modules are connected in series (PV
module string) and many such strings
are connected in parallel.
116 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Worksheet 5.6: A grid connected PV power plant is installed wherein PV modules are connected to
the grid through a grid-tied inverter. The voltage range for inverter operation is 300 – 400 V and maximum
current the inverter can handle is 150 A. Design a solar PV system for such inverter which should operate
at maximum voltage of 350 V and current at 150 A. The modules available for this are having Vm = 40 V,
Im = 9 A. Also, estimate the final power of the system.

Step 1 Note down the voltage, current and power requirement of PV module array:
PV module parameter Symbol Value Unit
PV array power requirement (peak power or Pma or Ima × Vma 350 × 150 = ______ watt
maximum power point)
PV module array open circuit voltage at peak Vma or Pma /Ima ______ ÷ ______ = ______ volt
power
PV module array current at peak power Ima or Pma /Vma ______ ÷ ______ = ______ ampere

Step 2 Note down the parameter of a PV module that is to be connected in PV array:

PV module parameter Symbol Value Unit
Open circuit voltage of PV module Voc (not given) volt
Short circuit current of PV module Isc (not given) ampere
Voltage at maximum power point Vm 40 volt
Current at maximum power point Im 9 ampere
Maximum power of PV module Pm = Vm × Im = ______ × ______ = ______ watt

Step 3 Estimating the number of PV modules to be connected in series and parallel:

PV module parameter Symbol Value Unit
Required PV array voltage at maximum power point Vma volt
Voltage at maximum power point of single PV module or PV Vm volt
string
Number of PV modules in series (Ns) Ns = Vma /Vm ____ ÷ ____ = ____ number
Current at maximum power point of PV array Ima ampere
Current at maximum power point of PV module or PV string Im ampere
Number of PV modules in series (Np) Np = Ima /Im ____ ÷ ____ = ____ number
≈ ____

Step 4 Estimating the total power of the series PV module array:

PV module parameter Symbol Value Unit
Number of PV modules in series (Ns) Ns number
Number of PV modules or module Np number
strings in parallel (Np)
New value of PV array voltage at Vma = Vm × Ns ____ × ____ = ____ volt
maximum power point
New value of PV array current at Ima = Im × Np ____ × ____ = ____ ampere
maximum power point
Maximum power of single PV module Pm = Vm × Im ____ × ____ = ____ watt
Maximum power of PV module array Pma = Pm × Ns × Np ___ × ___ × ___ watt
= Vm × Im × Ns × Np or  = ___ × ___ × ___ × ___
or = Vma × Ima or  = ___ × ___ = ___
 Chapter 5: Solar PV Module Arrays 117

Example 5.8 In a PV power plant of 1 MW capacity, a large numbers of PV modules are required
to be connected in series and parallel combinations. Design number of PV modules
to be connected in a series and in parallel for 1 MWp PV plant. In the PV power
plant, the desired voltage at maximum power point is 700 V. Estimate the current
at peak power point of the plant. Estimate the peak power that will be supplied by
one such PV module string. The parameters of PV modules to be used in the PV
plant are following: Voc = 44 V, Vm = 32 V, Isc = 8.5 A and Im = 7.5 A.
Solution Step 1 Note down the voltage, current and power requirement of PV module
array:

PV module parameter Symbol Value Unit

PV array power requirement (peak Pma or Ima × Vma 1000,000 watt
power or maximum power point)
PV module array open circuit Vma or Pma /Ima 700 volt
voltage at peak power
PV module array current at peak Ima or Pma /Vma 1000000 ÷ 700 ampere
power = 1428.57
≈ 1429

Step 2 Note down the parameter of a PV module that is to be connected in

PV array:

PV module parameter Symbol Value Unit

Open circuit voltage of PV module Voc (not given) volt
Short circuit current of PV module Isc (not given) ampere
Voltage at maximum power point Vm 32 volt
Current at maximum power point Im 7.5 ampere
Maximum power of PV module Pm = Vm × Im 32 × 7.5 = 240 watt

Step 3 Estimating the number of PV modules to be connected in series and

parallel:
PV module parameter Symbol Value Unit
Required PV array voltage at maximum Vma 700 volt
power point
Voltage at maximum power point of single Vm 32 volt
PV module or PV string
Number of PV modules in series (Ns) Ns = Vma /Vm 700 ÷ 32 number
= 21.875
≈ 22
Current at maximum power point of PV Ima 1429 ampere
array
Current at maximum power point of PV Im 7.5 ampere
module or PV string
Number of PV modules in series (Np) Np = Ima /Im 1429 ÷ 7.5 number
= 190.53
≈ 191
118 Solar Photovoltaic Technology and Systems: A Manual for Technicians, Trainers and Engineers

Step 4 Estimating the total power of the series PV module array:

PV module parameter Symbol Value Unit

Number of PV Ns 22 number
modules in series (Ns)
Number of PV Np 191 number
modules or module
strings in parallel (Np)
New value of PV Vma = Vm × Ns 32 × 22 = 704 volt
array voltage at
maximum power point
New value of PV Ima = Im × Np 7.5 × 191 ampere
array current at = 1432.5
maximum power point
Maximum power of Pm = Vm × Im 32 × 7.5 = 240 watt
single PV module
Maximum power of Pma = Pm × Ns × Np 240 × 22 × 191 watt
PV module array = Vm × Im × Ns or 32 × 7.5 × 22
  × Np    × 191
or = Vma × Ima or 704 × 1432.5
  = 1008480

Worksheet 5.7: In a PV power plant of 1 MW capacity, a large number of PV modules are connected
in series and parallel combinations. In such plants, 1 MW inverter can take input voltage in the range of 500 V
to 700 V. Design number of PV modules to be connected in a single series (PV module string) to obtain
voltage at maximum power point of 600 V. Also, estimate the peak power that will be supplied by one
such PV module string. The parameters of PV modules to be used are: Voc = 44 V, Vm = 35 V, Isc = 8 A
and Im = 7 A.

Step 1 Note down the voltage, current and power requirement of PV module array:
PV module parameter Symbol Value Unit
PV array power requirement (peak power or maximum Pma or Ima × Vma 10,00,000 watt
power point)
PV module array open circuit voltage at peak power Vma or Pma /Ima 600 volt
PV module array current at peak power Ima or Pma /Vma ____ ÷ ____ = ____ ≈ ____ ampere

Step 2 Note down the parameter of a PV module that is to be connected in PV array:

PV module parameter Symbol Value Unit
Open circuit voltage of PV module Voc (not given) volt
Short circuit current of PV module Isc (not given) ampere
Voltage at maximum power point Vm 35 volt
Current at maximum power point Im 7 ampere
Maximum power of PV module Pm = Vm × Im ____ × ____ = ____ watt
 Chapter 5: Solar PV Module Arrays 119

Step 3 Estimating the number of PV modules to be connected in series and parallel:

PV module parameter Symbol Value Unit
Required PV array voltage at maximum power point Vma 600 volt
Voltage at maximum power point of single PV module Vm volt
or PV string
Number of PV modules in series (Ns) Ns = Vma /Vm ____ ÷ ____ = ____ ≈ ____ number
Current at maximum power point of PV array Ima ampere
Current at maximum power point of PV module or PV Im ampere
string
Number of PV modules in series (Np) Np = Ima /Im ____ ÷ ____ = ____ ≈ ____ number

Step 4 Estimating the total power of the series PV module array:

PV module parameter Symbol Value Unit

Number of PV modules in series (Ns) Ns number
Number of PV modules or module Np number
strings in parallel (Np)
New value of PV array voltage at Vma = Vm × Ns ____ × ____ = ____ volt
maximum power point
New value of PV array current at Ima = Im × Np ____ × ____ = ____ ampere
maximum power point
Maximum power of single PV module Pm = Vm × Im ____ × ____ = ____ watt
Maximum power of PV module array Pma = Pm × Ns × Np ____ × ____ × ____ watt
= Vm × Im × Ns × Np or ____ × ____ × ____ × ____
or ____ × ____ = ____
or = Vma × Ima