Chapter Number 3.0 Solar PV modules Explained

A solar PV module is a collection of solar cells, mainly connected in series. These combinations of Solar Cell provide higher power than a single solar cell. The PV modules are available in the power rating range from 3 watt to 300 watt. They really from the basic building block of PV systems as power generating unit. With further connection of PV modules together, one can generate very large amount of power, in range of megawatt or MW. It is important to understand the making of a PV module parameters and measurement of PV module parameters are discussed. Output of a PV module depends on ambient conditions, the temperature and solar radiation intensity. The PV module power variation with the ambient condition variation is also discussed.

4.1 What is a Solar PV Module ?

A single solar cell can generate very less amount of power depending on the area of the cell. A single solar cell would generate  power in range of a fraction of a watt (like 0.1 watt) to few watt (like 2 to 3 watt). But in practice, the power requirements by our loads, like fan, TV, refrigerator, is in the range of several 100s of watt and sometimes more than 1000 watt or kilowatt (kW). When we talk about grid electricity and conventional power plans we talk about power in the range of millions of watts or MW. Therefore, a single solar cell is of no use for running the actual loads in home or supplying power to the electricity grid. We must generate solar  PV power in large amounts, in several watts, kW and MW. In order to fulfill the high power requirements, the number of cells are connected together to make a solar PV module. In this way, the solar PV module is a device which can supply larger power, larger than what individual solar cell can supply.

A single solar cell is shown in figure 4.1. It is shown to have typical shape of crystalline silicon solar cells, having lines across it which represent metal line of top contact. The cell is shown to have two terminals, a positive terminal and a negative terminal. Hen light falls on solar cells, voltage gets generated across these two terminals. In PV modules, many cells are connected together. The cells are connected in serial fashion, wherein positive terminal of one cell is connected to the negative terminal of the cell and this is repeated to make a string of solar cells, or a solar PV module (shown in Figure 4.2).

Voltage of cells strings connected in series 

When we connect cells in series, we get a string of solar cells. The string of solar cells will also have two terminals. When we connect cells in series the voltage of solar cells gets added, therefore, the terminal voltage of a PV string (PV module) will be higher and equal to the sum of all the solar cells connected in series. Suppose, terminal voltage of a solar cell is 0.5 V under operating conditions (shown in Figure 4.3) and two such identical cells are connected in series, so the terminal voltage of string of two solar cells will be 0.5 + 0.5 = 1 V. If 6 cells are connected in series, than terminal voltage of series of 6 cells will be 0.5 X 6 = 3 V (shown in Figure 4.3). If 36 solar cells are connected in series, then terminal voltage of series of 36 cells, or PV string of 36 cells will be 0.5 X 36 = 18 V.

EXAMPLE  4.1 A solar cell has terminal voltage of 0.75 volt under operating condition. What will be the terminal voltage of a PV module in which 28 cells are connected in series ?

Solution It is given that the terminal voltage of an individual cell under operating condition is 0.75 Volt.

Number of cells connected in series = 28

Total terminal voltage of the PV string of 28 cells or module = 28 X 0.75 = 21 volt.

Note: When we connect cells in series, voltage gets added and current remains nearly the same as that of individual cell and when we connect cell in parallel the current gets added but the voltage remain nearly same as that of a single cell.

4.2  Ratings of  PV Module 

The parameters of the solar PV modules (Voc, Isc, Wp), mentioned by the manufacturer are measured under some standard conditions of temperature (25°C) and solar radiation (1000 W/m2). These test conditions are known as standard test conditions (STC). The testing condition of STC is summarized in Table 4.1:

The most important parameter of a PV module is its peak output power. The solar PV modules are rated in terms of their peak power (Wp) output. It is the most important parameter from a user point of view. The  Wp is specified by the manufacturer under so-called standard test conditions (STC). The module rating under STC is widely accepted by the manufacturers and by the users.

Table 4.1 PV Module Testing Parameter Under Standard Test Conditions (STC)

Test Parameters	Values	Remarks
Solar Input Radiation	1000 W/m2	This solar radiation is corresponding to the condition when solar radiation travels 1.5 times the thickness of the earth’s atmosphere. Therefore, this radiation value is called Air Mass 1.5, and also referred as AM1.5 global solar radiation
Temperature	25 °C	This is cell temperature in the PV modules and not the PV module surface temperature. Normally, cells temperature in a PV module is much higher than PV modules surface temperature.
Wind speed	1 m/s	The flow of winds cools the PV module and that is why sometimes wind speed is also specified.

Departure from STC The conditions specified in the STC do not occur for most of the time and locations. This happens mainly because of two reasons; the real solar irradiation is normally less than 1000 W/m2 and the module temperature under real operation is more than the STC specified temperature of 25 °C. Both of these reasons result in lower module power output than the expected under the STC condition. The variation in output power of PV module with variation in input solar radiation and temperature is discussed in detail in Section 4.3.

4.3  Standard PV Module Parameters 

A PV module is made up of many cells connected together, and the electrical behavior of PV module is similar to PV cells. Therefore, the PV module parameters are also similar to solar cell parameters. In chapter 3, solar cell parameters have been discussed, which include; open circuit voltage (Voc), Short circuit current  ( Isc), maximum power point (Pm), voltage at maximum power point (Vm), current at maximum power point (Im,) fill factor (FF) and efficiency (ɳ) of the cells. A solar PV module also has same set of parameters. Most of the times all above parameters are mentioned in the datasheet of the modules supplied by a manufacturer. These electrical parameters of the PV modules are discussed here with the help of current –voltage curve or I-V curve and power-voltage curve or P-V curve.

4.3.1  I-V and P-V  Characteristic of  SPV Module 

The I-V characteristic of a SPV module is graph of current (I) and voltage (V) in which values of different current for different voltages is plotted on Y-axis and X-axis respectively. A typical I-V  curve of a PV module is shown in Figure 4.4. A P-V curve is plotted between power of a PV module on Y-axis and voltage of a PV module on X-axis. A typical P-V curve of a PV module is shown in Figure 4.4.

Short Circuit Current ( Isc)

It is the maximum current a solar PV module can produce. It happens when two terminals of a PV module is shorted, hence the name short circuit current. For a given solar cell area used in module, the higher the  Isc, the better is the PV module. It is measured in ampere (A). The value of this maximum current depends on PV module technology, PV module area, the amount of Solar radiation falling on PV module, angle of PV module with respect to the sun’s rays, etc. Many times, people are given current density rather than current. The current density is obtained by dividing the Isc by the area of solar PV module (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 solar PV modules produce. It happens when two terminals of the PV module left open, and hence name is open circuit voltage. For a given number of cells in series in a PV module, higher the Voc better is the PV module. It is measured in Volts (V). The value this maximum open circuit voltage mainly depends on PV module technology and operating temperature.

Maximum power point (Pm or Pmax)

It is the maximum power that a solar PV module produces under STC. For a given PV module dimensions, the higher the Pm , the better is the PV module. 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 PV module can operate at many current and voltage combinations. But a solar PV module will produce maximum power only when operating at certain current and voltage. This can be seen from the P-V curve of a PV module shown Figure 4.5. In Figure 4.5, the power axis is corresponding to current axis in I-V curve of module (Figure 4.4.). For comparison, I-V curve of the module is shown as dotted line on the P-V curve. Figure 4.5 indicates that at small voltages and current power output of a PV module is small. As the voltage increases, the power output increases and reaches a peak value corresponding to Im and Vm  of a PV module. This maximum power point is denoted in Figure 4.5 as Pm. If a PV module operates at voltage higher than Vm, the module output power decreases again (due to decrease in current) and at open circuit voltage (Voc), PV module power decreases to zero. Normally, the maximum power point for I-V curve of the solar PV modules occurs at the ‘knee’ or ‘bend’ of the curve. In terms of expression, Pm is given as :

Pm or Pmax = Im  X  Vm

Please note here that  Wp  or Pm or Pmax is the maximum power output under standard test condition. The maximum PV module power output Pmax is obtained only when solar PV module operates at certain current (Im) and voltage (Vm) in STC solar radiation condition of 1000 W/m2. If PV module operates at any other combination of current and voltage under STC, we will not get the maximum possible output power from the PV module as shown in Table 4.2. Similarly, at solar radiation condition other than STC (Solar radiation lower than 1000 W/m2), there will be only one combination of current and voltage at which the PV module output power will be maximum (but lower than Wp under STC). Thus, there exists a maximum power point corresponding to each input solar radiation, and not only for STC condition.

Table 4.2 Measured Current-voltage Data Points of a PV Module Corresponding to Figure 4.6.

Sr.no.	Current (A)	Voltage (V)	Power (W)
1	1	2.5	P1 = 2.4
2	0.9	6	P2 = 5.4
3	0.85	13.5	P3 = 11.475
4	0.65	15	P4 = 9.75
5	0.45	16	P5 =7.2

Current at Maximum power point ( Im )

This is the current which solar PV module will produce when operating at maximum power point. Sometimes, people write Im as  Imp  or  Impp. The Im will always be lower than Isc. It is given in terms of A. Normally, Im is equal to about 90% to 95% of the Isc of the module.

Voltage at Maximum power point ( Vm )

This is the voltage which solar PV module will produce when operating at maximum power point. The Vm  will always be lower than Voc. Sometimes, people write Vm as Vmp or Vmpp. It is given in terms of V.  Normally Vm is equal to about 80% to 85% of the Voc of the PV module.

Fill factor (FF )

As the name suggests , the FF is the ratio of the areas covered by  Im – Vm rectangle with area covered by Isc. – Voc rectangle (both shown by dotted line in Figure 4.4). It indicates the squareness of the  I-V curve. The higher the FF, the better is the PV module. The FF of PV module is given in terms of percentage (%). PV module with squared I-V curve is a better PV module.

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

Pm  = Isc X  Voc X  FF

Efficiency  (ɳ ) 

The efficiency of a solar PV module is defined as the maximum output power (Pm or Pmax ) divided by the input power (Pin). The efficiency of a PV module is given in terms of percentage (%), 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 the solar PV module area. Thus efficiency can be written as :

A module manufacturer provides most of the above module parameters in the form of their datasheets.

EXAMPLE  4.2 A solar PV module is fabricated using 36 solar cells of 155 cm2 connected in series. The cell have 35 mA/cm2 current density at Standard Test Condition (STC). Estimate the maximum current produced by the module at STC. 

Solution It is given that all the solar cellar are connected in series, therefore, current generated by one solar cell will be the current flowing in the string of 36 solar cells, which will be the current of the PV module. Therefore, in order to calculate the module current, we must calculate the maximum current (  Isc  at STC) of one solar cell. Current density of a solar cell is given by

Where,

Jsc  =  Current density (A/m2)

Isc =   Output current (A)

A  =  Area (cm2)

It is given that  Jsc = 35 mA/cm2, and cell area is 155 cm2.

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

Output current  (Isc) = Jsc X A = 0.035 A/cm2  X  155 cm2 = 5.42 A

Thus, the maximum PV module current, that is  Isc  (at STC) will be 5.41 A.

EXAMPLE  4.2 A small PV module having an area of 0.094 m2 gives a current of 0.71 A and voltage of 16.5 V at maximum power point under STC. What is the maximum power point of the SPV module ? Also, find out the efficiency.

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

Pm or Pmax = Im  X  Vm

Given that, Im  = 0.71 A

Vm = 16.5 V

Therefore, maximum power point, Pm = 0.71 A X 16.5 V = 11.71 W

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

Where,

ɳ = 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)

ɳ = ?

We know, Pm  = 10.06 W and at STC, Pin = 1000 W/m2

Now, we solve for efficiency,

Note: We need to multiply FF and Efficiency with 100 in order to present the result in percentage.

Reading PV module parameters from  I-V curve

In the preceding sections, the parameters of solar PV modules are defined using I-V and P-V curves. Therefore, if we have measured I-V curve of a PV module, we should be able to extract all parameters of PV module. A measured I-V curve of a crystalline Si PV module of 0.1 square meter area is given in Figure 4.6 and the measured data points (P1, P2, P3, P4, P5,) are given in Table 4.2.

• From figure 4.6 and Table 4.2, estimate the main parameters of  solar PV module.
• Short circuit current (Isc  ) : At 0 V (short circuit), the current of a module is 1 A (from figure 4.6), therefore, Isc  = 1 A.
• Open circuit voltage (Voc) : At 0 A (open circuit), the voltage of the module is about 18 volt, therefore, Voc = 18 V.
• Maximum power point (Pm) : from table 4.2, the value of maximum  power is 11.47 watt.
• Current at maximum power point ( Im) : From Table 4.2, the current at maximum power point is 0.85 A.
• Voltage at maximum power point (Vm) : from Table 4.2, the voltage at maximum power point is 13.5 V.
• Fill Factor (FF) : It can be calculated using the expression for FF :
•   Efficiency (ɳ) : It can be calculated from the given parameters.

Here, the Pn is input power corresponding to STC, which is 1000 W/m2.  Thus, feeding the parameters in above equation, we get.

In this way, one can estimate all parameters of PV module from its I-V curve.

WORKSHEET  4.1 : 

Comment on the values of Voc, FF and Efficiency of the PV module given in Figure 4.6 whether the values are as per your expectations, smaller or larger, etc.

Comments :

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4.3.2  How Many Cells in Module ?

The module manufacturing technology was developed aggressively in the 1980s. At that time , the PV modules were designed for charging batteries of 12 V terminal voltages. Therefore, one of the modules requirements is to provide sufficient voltage to be able to charge 12 V batteries under typical daily solar radiation. Now, voltage source will be able to charge battery if the source voltage is higher than the battery voltage. It means that the module voltage, under daily radiation conditions should be higher than the battery voltage. Generally, it is expected that the PV module must provide about 15 volts (or around this value) in all operating conditions, meaning low solar radiation (like in morning and evening) and high temperatures (like in summer).

PV module design for 12 V battery level has now become standard. For large power module, the design is done for 24 V battery level (two batteries in series), 36 V battery level (three batteries in series), etc. or, we can say the PV modules are designed to provide voltages in a multiple of 12 V battery level, that is 12 V, 24 V, 36 V, 48 V, etc. We must note here that for 12 V batteries voltage level, PV module (Vm) should be around 15 V, and for 24 V battery voltage level, PV module voltage should be around 30 V. Similarly, for 36 V battery voltage level, PV module voltage should be around 45 V. Also, note here that when we refer to the module voltage level, we refer to the module voltage at maximum power point. Table 4.3 shows the possible voltage level of batteries and corresponding voltage levels of PV modules. Considering this, the other electronics devices used in PV systems also follow the similar voltage levels. For  instance, charge controller, MPPT and inverter are designed in such a way that they can take input voltage in multiples of 12 V, i.e., 12 V, 24 V, 36 V etc. battery voltage levels or 15V, 30 V, 45 V, etc. PV module voltage level (Vm).

Table 4.3 Voltage levels for Combination of Batteries and corresponding Voltage Level (Vm) Required from Combination of PV Module

Battery Voltage  (single battery or series combination of batteries)	Corresponding PV module voltage levels, at maximum power point condition (single module or series combination of modules)
12 V	15 V
24 V	30 V
36 V	45 V
48 V	60 V

Since single solar cell provides smaller voltage, it is required to connect many solar cells in series to get higher PV module voltage to charge a battery. As mentioned earlier, there are different technologies of Solar PV cells. Depending upon each technology, the number of cells to be connected in series is decided. The decision of ‘how many cells to connect in series in a PV module’ is determined by Voc of the cell. Voc  of a single solar cell for various solar cell technologies has been mentioned in Table 3.4 in Chapter 3.

For crystalline silicon solar cell technology, required voltage for charging 12 V battery v=can be obtained by the series connection of 36 solar cells.  Why 36 cells in series ?  Commercial Si solar cells generally have a Vm of about 0.5 volts at 25°C. We also known that due to higher operational temperature (higher than specified by STC, 25°C), the voltages (Vm and Voc) decrease. The solar cell under encapsulation operates at higher temperature resulting in loss of voltage (as discussed in chapter 3) by about 0.08 V.

Thus available cell terminal voltage

Vm = Vm (STC) – loss of voltage due to higher temperature.

= 0.50 – 0.08 = 0.42 V

Now, we want about 15 volt module output voltage in all conditions, and each solar cell will give us about 0.42 V. Now, in order to calculate number of cells to be connected in series, required voltage must be divided by possible operating voltage from one cell.

Number of cell in series =

Note:  Estimation of the number of cells in a module depends on the Vm and loss of voltage due to temperature, both of these depend on the cell technology. Thus, with the technology, the number of cells to be connected in series to get desired voltage can change. If Vm (STC) is higher, we need less number of solar cells in series and if Vm (STC) is lower, we need more number of solar cells in series to get desired operating voltage.

A schematic diagram and actual photograph of a typical crystalline Si PV module having  36 cells is connected in series is shown in Figure 4.7. The symbol of module is given in Figure 4.8 and it shows positive and negative terminals, peak power, and current and voltage at peak power.

In this way, one can estimate the number of cells in series for any PV module voltage requirement and for any PV technology.

Nowadays, solar PV modules are also available to charge 6 V and 3 V batteries. Since the battery terminal voltage is lower, the module voltage requirement will also be lower and the number of cells one must connect in series will also be lower.

Procedure to estimate or design number of cells in a module.

Thus, in order to estimate the number of cells in a PV module, one can use following steps :

Step 1 : Find out the Vm (STC) of a solar cell of given technology (if Vm  is not given, it can be estimated by Voc); the PV module parameters Vm and Voc) are discussed in the next section.

Step 2 : Find out loss of voltage (loss of Vm) under operating conditions.

Step 3 : Available voltage at operating conditions = Vm (STC) – Loss of voltage.

Step 4 : Note down the required PV module voltage.

Step 5 : Divide the required module voltage by available operating voltage to get the number of cells connected in series.

EXAMPLE  4.4 A PV module of new solar cell technology is to be designed to charge a battery of 12 V. The Voc  and Vm of the cell of new technology under STC are 0.90 and 0.80 respectively. The cells voltage decreases by 1 mV every degree centigrade rise in temperature. How many cells should be connected in series in this PV module, if cell temperature under operation is 600C. Make a drawing of PV module with this new technology.

Solution Let us estimate the number of cells as per the procedure given above.

Following parameters are given :

Vm  of new solar cell = 0.80 volt

Battery voltage = 12 V

Cell operating temperature = 600C

Per degree centigrade decrease in voltage = 1 mV or 0.001 V

Step 1 : Find out the Vm (STC) of a solar cell of given technology  Vm  (at STC) =  0.8 V.

Note : If Vm  is not given, it can be estimated using Voc , typically, Vm is about 80% to 85% of Voc for all technologies.

Step 2 : Find out loss of voltage (loss of Vm) under operating conditions. The temperature corresponding to STC is 250C, the cell is operating at 600C, therefore, the cell is operating 60-25 = 350C above STC.

Loss in voltage per degree centigrade rise in temperature is 0.001 V,

Therefore loss of voltage due to 350C  rise in temperature = 0.001 X 35 = 0.035 volt.

Step 3 : Available voltage at operating conditions = Vm (STC) – Loss of voltage.

Available voltage at operating conditions = 0.8 – 0.035 = 0.765V.

Step 4 : Note down the required PV module voltage.

The battery to be charged is 12 V, therefore, the PV module voltage in all operating conditions should be about 15 V.

Required PV module voltage = 15 V.

Step 5 : Divide the required module voltage by available operating voltage to get the number of cells connected in series.

Number of new type of cells to be connected in series =

Thus 20 type of cells must be connected in series to get sufficient voltage to charge 12 V battery in all operational conditions (draw 20 cells connected in the series in space shown below).

EXAMPLE  4.5 A manufacturer using advance crystalline silicon cell technology produces the solar cells with Voc  of  0.620 V and Vm of 0.510 V at STC. Cell temperature reaches to about 600C in operating conditions. The modules are designed to connect in grid connected PV plant. If required operating voltage of module is 13.5 V, then estimate the number of cells to be connected in series.

Solution Let us estimate the number of cells as per the procedure given above.

Following parameters are given :

Vm  of new solar cell = 0.510 volt

Cell operating temperature = 600C

Per degree centigrade decrease of voltage for crystalline silicon cell = 0.0023 V.

Step 1

Step 1 : Find out the Vm (at STC) of a solar cell of given technology  Vm  (at STC) =  0.510 V.

Note : If Vm  is not given, it can be estimated using Voc , typically, Vm is about 80% to 85% of Voc for all technologies.

Step 2 : Find out loss of voltage (loss of Vm) under operating conditions. The temperature corresponding to STC is 250C, the cell is operating at 600C, therefore, the cell is operating (60-25) 0C = 350C above STC.

Loss in voltage per degree centigrade rise in temperature is 0.0023 V,

Therefore loss of voltage due to 350C  rise in temperature is  = 0.0023 X 35 = 0.080 volt.

Step 3 : Available voltage at operating conditions = Vm (STC) – Loss of voltage.

Available voltage at operating conditions = 0.510 – 0.080 = 0.430V.

Step 4 : Note down the required PV module voltage.

Required PV module voltage = 13.5 V (given)

Step 5 : Divide the required module voltage by available operating voltage to get the number of cells connected in series.

Number of new type of cells to be connected in series =  or about 32 cells.

Thus, in this case, only 32 cells must be connected in series to get sufficient voltage.

Note : Sometime when we need to get higher output voltage from a PV module, higher than 15 V or so, we need to connect more cells in series. When we need lower output voltage we connect fewer cells in series. These days high power modules (more than 100 Wp) with 60 to 70 cells connected in series are also available in the market. Sometime less wattage modules (<10 Wp) will have only 18 cells in series.

4.3.3  Estimating or Designing Wattage of a PV Module.

Wattage of PV module is one of the most important parameter from user perspective. When a user buy a PV module from a market, the cost of the PV module is given in terms of Wattage that a PV module can generate. Normally ,the PV module output power changes with the solar radiation intensity, which changes throughout the day, therefore, all manufacturers rate the PV module power output under one certain condition, which is known as Standard Test Condition (STC). The STC is corresponding to 1000W/m2 of solar radiation at 250C of cell temperature. Under this condition, if the PV module is operating at maximum power point, the output power of the module is known as ‘Peak power’ and written as wattpeak  or Wp. Normally, the solar radiation intensity is lower than 1000 W/m2 and cell temperature under operation is higher than 250C; both of these effects decreases the power output of module. Thus, in almost all operating condition, the actual output power of PV module is less than the rated peak power or Wp of PV module given by manufacturer. Anyway, the question is how to estimate the peak power or Wp of a PV module ?

The output power of a PV module depends on the voltage and current at which the module is operating. As discussed earlier, if the module operates at current Im and voltage  Vm, then the power generated (Pm) by the PV module is maximum. The estimation of Vm of the module is discussed already in section 4.3.1 of this chapter. Let us now learn to estimate the Im of a PV module. In chapter 3 about solar cells. It is mentioned that the current generated by a solar cell depends on area of the cell. Similar area solar cell produce small current and large area solar cell produces large current. A parameter called current density, which is current divided by area, is independent of the cell area. In chapter 3, Table 3.4, the typical current density of solar cells of different technology is given. For instance, for crystalline silicon solar cell technology, the current densities (Jsc) of commercial cells are in range of 30 to 35 mA/cm2 (given under STC), and the size of solar cells can vary from small 5 cm2  cells to large 225 cm2 cells. Thus, knowing cell area and current density of cell of given technology, we can estimate the current that a cell produces under STC condition, that is, Jsc X A, and this current will be nothing but Isc.

In the module, since cells are connected in series, normally, in the module designed for 12 volt operation, the current produced by a single solar cell is the current of the PV module. Thus, if a large area cell is producing 5 A (Isc) current, if there are 36 identical cells connected in series, the Isc of the PV module will also be 5 A.

EXAMPLE  4.6 A manufacturer of crystalline silicon  solar cell guarantees 33mA/ cm2 current density of his solar cells. If the cell area is 144 cm2, then estimate the Isc  of solar cell.

Solution It is given that :

Cell area is  = 144 cm2

Current density Jsc = 33 mA/cm2 or 0.033 A/cm2

Therefore,

Isc = Jsc  X A 

= 33 mA/cm2 X  144 cm2

= 0.033 A/cm2 X  144 cm2 = 4.75 A

EXAMPLE  4.7 A manufacturer of cadmium  telluride solar cell  guarantees  25 mA/cm2 current density of his solar cells. If the cell area is 100 cm2, then estimate the Isc  of solar cell.

Solution From the above calculation, one can estimate the  Isc  of the module. But in order to calculate the Pm of the module, we need to estimate Im . Normally Im  is equal to about 90% to 95% of the Isc of the module, and normally Vm  is equal to about 80% to 85% of the Voc of the PV module.

EXAMPLE  4.8 A cell mentioned in Section 4.1 is used to make a solar PV module wherein 36 cells are connected in series.  The PV module has the Vm  of 15 volt. Estimate the Pm of the module.

Solution It is given that :

Vm of the module : 15 volt.

Isc of single cell = 4.75 A

Assuming that Im = 95 % of Isc = 0.95 X 4.75 = 4.51 A

Thus, the Pm of the module will be :

Pm = Im  X  Vm = 4.51 X 15

    = 67.7 watt.

WORKSHEET  4.2 : Some PV module parameters are given in Table 4.4. Fill in the blanks by estimating the other PV module parameters. Assume Vm = 0.85 X Voc  and Im  = 0.93 X Isc . All the parameters are given at STC.

Table 4.4 PV Modules Parameters

Voc  (volts)	Vm  (volts)	Isc (ampere)	Im  (ampere)	Cell area (cm2)	Pm (watt)
21	–	5.0	–	145	–
–	13.5	2.0	–	55	–
–	14.5	–	0.8	30	–
19	–	–	1.5	50	–
–	14.2	–	3.2	100	–
–	15	5.7	–	160	–

Table 4.5 Table of problem 4.1

S.No	Parameters	Reading or calculating from figure 4.9	Values of parameter	Unit of parameter
1	Short circuit current (Isc)	Current value when voltage is zero
2	Open circuit voltage (Voc)	Voltage value when current is zero
3	Maximum power point (Pm)	Value of maximum power
4	Current at power point (Im)	Current value at maximum power point
5	Voltage at power point (Vm)	Voltage value at maximum power point
6	Fill Factor (FF)
7	Efficiency (ɳ)

WORKSHEET  4.3 : Current and voltage of a PV module is measured at various operating points. Estimate the power that can be produced at each operating point. Using these calculations, fill the solar PV module parameter in Table 4.6.

Table 4.6 To Obtain Power

S.No.	Current I (A)	Voltage V (V)	Power P (W) = I x V
1	0	37.72	–
2	0.25	37.58	–
3	0.44	37.15	–
4	0.46	37.04	–
5	0.53	36.77	–
6	0.60	36.53	–
7	0.69	35.97	–
8	0.86	35.02	–
9	1.06	33.77	–
10	1.37	29.32	–
11	1.48	16.73	–
12	1.50	00.00	–

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 power point (Im)
5	Voltage at power point (Vm)
6	Fill Factor (FF)
7	Efficiency (ɳ)

4.4  Factors Affecting Electricity Generated by a Solar PV Module

Let us now discuss how in practical applications the PV module power output varies with variation in ambient conditions like temperature, solar radiation, angle of sunrays, etc. The change in PV module parameter output power with change in ambient condition is important to understand. This will be useful in estimating the 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 (ɳ).
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. (0)

4.4.1  Effect of Conversion Efficiency (ɳ)

The modules consist of several cells electrically interconnected to each other in series 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 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 result 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 (ɳ) of module can be given as:

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, 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.

Where,

ɳ =  Efficiency in percent (%)

Pm or Pmax = Output power in watt (W)

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

A = Solar cell area in square meter(m2)

ɳ = 22, 17, 16, 12 (in %)

Pin = 1000 W/m2

A = 58.7 X 39.0 (inch)2.

Pm = ?

First, we convert cell area from (inch)2 to m2

We know, 1 inch = 0.0254 meters.

58.7 inch = 1.49 meter and 39.0 inch = 0.99 meter

Therefore, module area (A) = 1.49 X 0.99 = 1.475 m2

Now, we solve for solar cell of efficiency 22%

Above equation can be written as :

Pm  =  ɳ X Pin X A

We put the respective terms values and we get,

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

ɳ (%)	Pin (W/m2)	A (inch)2	A (m2)	ɳ /100	Pm  = ɳ /100 X Pin X 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 a module as shown in figure 4.11.

4.4.2  Change in the Amount of Input Light (Pin)

We should keep in mind that the amount of sunlight (intensity of sunlight), falling on solar PV module depends on the amount of light falling on it. The electric current generated by solar PV is directly proportional to the amount of light falling 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, current output of a solar PV module also increases from morning till afternoon. From morning till 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 X 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 figure4.12. 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 250C cell temperature and foe 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 power or maximum power point is shown by ‘X’ in Figure 4.12. The actual power output from a PV module may be lower than the maximum power point, if the PV module is not operating at current and voltage corresponding to maximum power point (as discussed in Section 3.2.1.)

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 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

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

Remains 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

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

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.

4.4.3  Effect of Change in PV Module Temperature

The solar PV modules output voltage, power & efficiency ratings are given at standard test condition (STC = 1000 W/m2 and 250 C.). The PV module output voltage, PV module efficiency and output power depends on the cell temperature in PV module. In practical applications, the operating temperature of solar cells in PV modules may be different than 250 C. The cell temperature varies due to ambient temperature. In many cases, the ambient temperature is higher than the STC temperature of 250 C. Moreover, in practice, the cells in 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 module decreases, which results in decrease in PV module efficiency and PV module output power.

The change in PV module parameters with increase in cell’s operating temperature (or temperature coefficient of PV module parameters) in PV module 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 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 0 C Rise in cell Temperature From Standard Test Condition (STC) Value of 250C (The PV module parameters of various commercially available technologies are given)

PV Technology name	Typical Value of change in parameter value per 0C rise in cell temperature from standard test condition (STC) value of 250C (+ indicates increase, – indicates decrease)
	Temperature coefficient of current (Isc)	Temperature coefficient of voltage (Voc)	Temperature coefficient of Fill Factor (FF)	Temperature coefficient of power (Pm)
Crystalline silicon	+0.08% / 0C	-0.35% / 0C	-0.15% / 0C	-0.45% / 0C
Cadmium telluride	+0.04% / 0C	-0.25% / 0C	-0.035% / 0C	-0.25% / 0C
Double junction	+0.07% / 0C	-0.03% / 0C	-0.095% / 0C	-0.25% / 0C
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 ratings 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 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 co-efficient 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 :

P(temp)  = P(stc) – TC X P (stc)  X Δ T

Using the above formulae, one can find the change in any parameter value for any given cell operating temperature. The above formula can be written for any parameter. For instance, The formulae for change in maximum module voltage due to increase in cell temperature in PV module will be given as :

Vm (temp)   = Vm (stc)  – TCvoltage X Vm (stc) X Δ T

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  X  Pmax  (stc) X Δ T

Table 4.11 Different Values of Module Output at Different Temperatures

S.No.	Temperature (0C)	Wattage (watts)
1	25 (STC)	75.0
2	30	73.3
3	40	69.9
4	50	66.6
5	60	63.2
6	70	59.8

WORKSHEET  4.3 :  The maximum rated power point of a crystalline silicon solar cell is 75 Wp. Calculate the maximum power output at 450C , 550C and 650C cell operating temperature. For crystalline silicon, cell decrease in maximum power per degree centigrade increase in cell temperature, (from STC value of 250C) is  -0.45% / 0C. Fill Table 4.12.

Use the following equation:

Actual Pmax  at cell operating temperature (watt)

Pmax (temp)   = Pmax  (stc)  – TCpower  X  Pmax  (stc) X Δ T

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

Opearating cell temperature (0C)	STC cell temperature (0C)	Δ T (0C)	Pmax  (stc)  (watt)	TC (%)	TCpower  X  Pmax  (stc) X Δ T (watt)	Pmax (temp)  (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 600C ? 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 250C.

The operating temperature of the PV module at which Vm needs to be calculated is 600C, i.e., we need to calculate Vm, (600C).

The difference in operating PV module temperature and STC temperature

Δ T = 60-25 = 350C 

Now, considering Table 4.10 the decrease in voltage per degree centigrade rise in PV module temperature from standard test condition (STC) value of 250C is -0.35%

Now using the formulae for estimating change in the voltage due to temperature increase

Vm (temp)   = Vm (stc)  – TCvoltage X Vm (stc) X Δ T

4.4.4  Change in PV Module Area (A)

Generally, the modules of a large area give high power compared to the modules 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 has increases or decreases with the increase or decrease in the number of cells in a module. For example in a module there are 36 cells and the area of each cell is 156 cm2 then total area of 36 cells = 36 X 156 = 562 cm2 = 0.562 cm2. Now, if the number of cells in same module is increased to say 72 cells then the total area of 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 , 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).

From above example , the questions arises ; why has the output voltage and output power doubled with the increase in module area ? This is because  Vm  and  Im of modules depends on the series or parallel types of cells interconnectivity used. When 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 string 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 string of cells in a module are inter-connected in series, high output voltage is obtained. When the string of cells in a module are interconnected 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 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 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 change in the area of module, the output power of the modules also changes.

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 comparison of Commercially available modules of different wattages at STC along with A, Vm , Im and ɳ  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 (ɳ)	36	54	60	72

4.4.5  Change in Angle of Light Falling on PV Module Area (Ɵ)

Similar to the solar cells discussed in chapter 3, the angle of sunlight with respect 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 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 a way (i.e., angle of module inclination) that most of the time sunlight is close to perpendicular, especially in the afternoon time when the intensity of sunlight is high.

4.5  Measuring Module Parameters

The module parameters mentioned in Section 4.3 can also measured or calculated based on some measured parameters. The parameters that can be measured by means of the measuring devices like open circuit and maximum voltage, short circuit and 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 equipment’s are required :

1. Ammeter or a multimeter.
2. Voltmeter or a multimeter.
3. Rheostat
4. Connecting wires.

4.5.1  Measuring Voc and Isc

The open circuit voltage (Voc) and short circuit current (Isc) can be directly measured 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.

Isc  measurement 

When you are measuring Isc  or short circuit current of a module, there should not be any load connected to the module, it should be in short circuit condition. For measuring Isc  using a multimeter, first put the probes of multimeter into the current measurement slots given in multimeter, and then set the multimeter knob to appropriate current range according to the module rating. The typical Isc  values of modules could be in range starting from 0.1 A to 10 A. Then connect the opposite polarity terminal of multimeter / ammeter and SPV module directly as shown in Figure 4.17. The reading shown by multimeter / ammeter in this case is short circuit current of the given SPV module. If a negative sign is shown in the meter with some reading. It indicates that the appropriate polarity of the module terminal and meter terminal is not connected. Reverse the connection and then measure again.

Measuring I-V curve (Vm and  Im )

This is the very useful measurement for any solar PV module to measure its performance in the laboratory as well as on the field in real time. The measurement would require two multimeters (or a voltmeter and an ammeter )and a rheostat. Make the electrical connections as shown in Figure 4.18. For measuring I-V  curve, the solar PV module has to be connected in series with the Rheostat, i.e., negative terminal of a solar PV module to the one end of rheostat and other end of rheostat should be connected to the positive terminal of the multimeter / ammeter. The negative terminal of the multimeter / ammeter should be connected to the positive terminal of the SPV module. The voltmeter or multimeter for voltage measurement is directly connected across the SPV module. If, by mistake, the connection of positive and negative terminals of voltmeter and ammeter is not done properly, it is not a problem, the difference however would be that the meters will show readings with negative sign. If the sign of reading are negative, make changes in connections.

After making the connections, now you are ready to make the measurements. Make a Table as shown in Table 4.14 to note down the readings. Make the table with three columns one for the serial number, one for noting down the voltage and one column for noting down the current. One extra column should be kept empty to make calculations for power (current X Voltage). After doing all the connections, in order to start the measurement, slide the rheostat at one side where the voltage should be maximum and current should be minimum, and note down the values of current and voltage at that instant , and note the readings in Table. Now, slightly slide the rheostat, readings of current and voltage will change. Note down the readings again. Keep on sliding the rheostat (and noting the readings) until knob of the rheostat reaches the other end.

Table 4.14  Table for Noting the current and Voltage Values from I-V Curve measurement of PV modules

S.No.	Current (A)	Voltage (V)	Power (W) = Current X Voltage
1
2
3
4
5
–
–
–

Noting and calculating module parameters

From the measured data point for I-V  curve all the parameters related to PV module can be calculated. Using Table 4.14 one can make a table of parameters of PV modules by noting the values in Table 4.15.

Table 4.14   Calculating Module Parameters

S.No.	Parameters	Reading or calculating from Table 4.14
1	Short circuit current (Isc)	Current value when voltage is zero
2	Open circuit voltage (Voc)	Voltage value when current is zero
3	Maximum power point (Pm)	Value of maximum power
4	Current at power point (Im)	Current value at maximum power point
5	Voltage at power point (Vm)	Voltage value at maximum power point
6	Fill Factor (FF)
7	Efficiency (ɳ)

Note : Im is normally 90 % to 95 % of Isc and Vm is normally 80 % to 85 % of Voc  for nearly all technologies.

EXAMPLE  4.13 Count the number of cells connected in series in the module shown in Figure 4.19 and calculate the open circuit voltage (Voc) and voltage at maximum power point (Vm). It is given that open circuit voltage of a single cell is 0.6 V.

 Solution Number of cells to be connected in series (ɳ) =

Total series open circuit voltage (Voc) =  Voc (single cell) x number of cells in series.

Voc (module) = _________ X ________

Voc (module) = _________ volts

Vm is normally 80% to 85 % of Voc. Let us assume that Vm =______ Voc

= __________V

Therefore, Vm (module) = ___________ volts.

4.5.2  Higher Wattage Modules

The crystalline Si cell technology is the most commonly used technology. For this technology, the large area solar cells are available in either size 12.5 X 12.5 cm2. Or 15 X 15 cm2. These size of solar cells are commonly used, particularly, in all modules which are used in grid-connected PV plants. Crystalline silicon cells with larger than this area are not available. How much peak power or Wp these modules can provide ? What to do if we want more power output per module ?

We now know that the PV modules are typically designed to produce about 15 volt (Vm) under operating conditions. And in order to get this voltage, there are about 32 to 36 cells connected in series (depending on Vm of individual cells and operating temperature). The current produced by the cells depends on the area and current density. The current density of commercially available crystalline Si solar cell is about 30 mA/cm2 to 35 mA/cm2 . Let us take 35 mA/cm2 here for estimation, relatively towards bit higher side. Thus, the maximum possible short circuit current (Isc) that we can get from modules with large area solar cell is :

Isc = Jsc ( mA/cm2) X Area (cm2)

=  35  X 12.5 X 12.5

= 5468 mA = 5.46 A

Isc = Jsc ( mA/cm2) X Area (cm2)

=  35  X 15 X 15

= 7875 mA = 7.87 A

We know that Im is normally about 90 to 95 % of the Isc. Let us assume 90% here for calculations.

Therefore, Im = 0.09 X Isc

Im = 0.90 X 5.46 = 4.91 A (for 12.5 X 12.5 cm2 cells)

Im = 0.90 X 7.87 = 7.08 A (for 15 X 15 cm2 cells)

Now, the maximum wattage (Wp) that we can get using these  two types of cells are :

Wp = Im X Vm

Wp = 4.91 X 15 = 73.65 watt

Wp = 7.08 X 15 = 106.2 watt

Using the best available crystalline Si cell technology with large area solar cells, the maximum possible wattages possible are 73.65 watt (15 V, 4.91 A, 12.5 X 12.5 cm2 cells) and 106.2 watt (15 V, 7.87 A, 15 X 15 cm2 cells).

The modules designed above can be used for 12 volts system voltages. In order to get higher voltages, two or more modules are connected in series. In order to get more current, two or more modules are connected in parallel. In this way, by making series and parallel connection, voltage and current of a PV system as well as power of a PV system can be increased.

We can increase the power output of crystalline silicon PV modules more than what we have just calculated in this section. A single solar cell provide Vm of about 0.5 V, the modules of 15 V (Vm) are obtained by connecting many individual cells in series. We can extend the same logic further. Higher voltage modules (higher than 15 V) can be designed by connecting a large number of cells in series, in this case, larger than 30 to 36 cells normally connected in the case of crystalline silicon cell technology. Thus by connecting more cells in series we can get higher voltage, and thus, higher power from the module. In similar way, if we connect more cells or string of cells in parallel, we can get more current and in this way, more power from the modules.

EXAMPLE  4.14 Design a Solar PV module for providing voltage at maximum power point of Vm 30 V (STC), and 28.5 V (under operating conditions, 550C  cell temperature). Use the cells with open circuit voltage of 0.62 V, and 0.002 V decrease in Vm per degree centigrade rise in temperature.

Solution We can use step by step method (refer to Section 5.1) to estimate the number of cells required in a module.

Step 1 : Find out Vm (at STC)of solar cell of given technology.

If Vm (at STC) is not given; we can estimate  Vm using Voc  value.

Assume Vm is about 80% to 85% of the Voc. Let us assume Vm = 0.80 X Voc

Vm  (cell)  = 080 X Voc (cell)  = 0.80 X 0.62 = 0.496 volts

Step 2 : Find out loss of voltage (loss of Vm) under operating conditions. The temperature corresponding to STC is 250C, the cell is operating at 600C, therefore the cell is operating 55-250C = 350C above the STC.

Loss in voltage per degree centigrade rise in temperature is 0.002 V.

Therefore loss of voltage due to 350C rise in temperature = 0.002 X 30 = 0.06 volt

Step 3 : Available voltage at operating conditions = Vm (STC) – Loss of voltage .

Available voltage at operating conditions = 0.496 V – 0.06 V = 0.49 V

Step 4 : Note down the required PV module voltage .

Required PV module voltage = 28.5 V (given).

Step 5 : Divide the required module voltage by available operating voltage to get the number of cells connected in series.

Number of new type of cells to be connected in series:

Normally, in the commercially available PV modules of large power, there are 60 cells connected in series as shown in Figure 4.20.

Amount of peak power generated from large modules ?

Now let us estimate how much power these modules with 60 cells connected in series (as shown in Figure 4.20) can generate under STC condition. Thus, now considering Vm (STC) of 30 V and considering the same values of Im for two size of solar cells as shown in Previous calculations) :

Im =  4.91 A (for 12.5 X 12.5 cm2 cells)

Im = 0.90 X 7.87 = 7.08 A (for 15 X 15 cm2 cells)

In this way, peak power output of a solar  PV module  will be :

Wp = 4.91 X 147.3 = 723.24 watt

Wp = 7.08 X 212.4 = 1503.79 watt

Thus depending on the size of solar cell, significantly  large power can be generated using single PV module. Again, depending on the requirement of even larger power (as in big PV plants), these modules can again be connected in series and parallel to get more power output. However since the power output of these modules are large, fewer connection would be required to get a given power output. These types of large PV modules are normally used in PV power plants of MW scale or of several MW sizes.

EXAMPLE  4.15 A SPV high power module is having an area of 1.62 m2 gives a current at maximum power point of 7.83 A and voltage at maximum power point of 29.4 V. The short circuit current of the module is 8.52 A and open voltage at maximum power point of 29.4 V. The short circuit current of the module is 8.52 A and open circuit voltage is 36.7 V. What is the fill factor, maximum power point and efficiency of the solar cell ? Consider STC.

Solution Following parameters of the module are given :

Short circuit current (Isc) = 8.52 A

Open circuit voltage (Voc) = 36.7 V

Current at maximum power point (Im) = 7.83 A

Voltage at maximum power point (Vm) = 29.4 V

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

Area (m2) = 1.62 m2

Now,

Maximum power point

Pm  or Pmax = Im X Vm  = (8.52 X 29.4) = 250.48 watt

Fill factor

Note : We need to multiply FF and efficiency with 100 in order to present the results in percentage.

EXAMPLE  4.15 A SPV module having total area of 1.646 m2 and gives a current of 8.08 A and voltage of 29.72 V at maximum power point. The short circuit current of the module is 8.48 A and open circuit voltage is 37.34 V. What is the fill factor, maximum power point and efficiency of the solar cell ? Consider STC.

Solution Following parameters of the module are given :

Short circuit current (Isc) = 8.48 A

Open circuit voltage (Voc) = 37.34 V

Current at maximum power point (Im) = 8.08 A

Voltage at maximum power point (Vm) = 29.72 V

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

Area (m2) = 1.646 m2

Now,

Maximum power point

Pm  or Pmax = Im X Vm  = (8.08 X 29.72) = 240.13 watt

Note that, the power of the module is very high, i.e. 240. 1 Wp. Such modules are available these days in the market.

Note : We need to multiply FF and efficiency with 100 in order to present the results in percentage.

Bypass diode

In solar PV modules, in almost all cases, all the solar cells, identical in nature, are connected in series. When light falls on a PV module, same current is generated in all solar cells which flow through PV module. Now, due to some reason, if one of the solar cells gets shaded (no light falling on one cell), then the current generated by the cell will be lower than the rest of the solar cells. Since the cells are connected in series, the shaded solar cell (generating low or no current) will resist the current flow generated by non-shaded solar cells generating full current. In this case, the shaded solar cell becomes a load for the other cells, and the power generated by other solar cells may get dissipated in the shaded solar cells. Due to this the shaded solar cell can become very hot, forming hot spots in the PV module. The hotspots sometimes can give rise to breaking of glass cover in PV module or in a worst case, it can cause fire. Therefore, local heating of solar cells in a PV module due to shading should be avoided.

Bypass diode is used to avoid the destructive effect of hot spots or local heating in series connected cells in PV modules. A diode, called bypass diode, is connected in parallel with solar cells with opposite polarity to that of a solar cell as shown in Figure 4.21. Thus, in normal condition (no shading), the bypass diode is operated in reverse bias condition, effectively in open circuit. But if a series is connected cell is shaded, reverse bias will appear across it. This reverse bias will act as a forward bias voltage for bypass diode since it is connected with opposite polarity. In this way, the bypass diode will carry the current, rather than shaded cell (meaning bypassing the current from shaded cell). By bypassing the current, the solar cell gets protected by heating and causing permanent damage to the PV module.

Ideally there should be each diode for the each solar cell in the solar PV module, but practically, due to cost reason, there are few bypass diodes which are connected in PV module. It is recommended that practically, there should be atleast one diode for each series combination of 10-15 cells. This connection is shown in Figure 4.22.

Blocking diode

In standard PV systems, PV modules are used to either supply the load during day time or to charge a battery. When there is no sunlight, like in the night, the SPV modules stop producing the energy and become idle. During night, charged batteries star supplying energy to the SPV modules. This is loss of energy and should be avoided. In order to avoid the flow of current from battery to solar PV modules, a diode, called blocking diode is used to block the current flow. Thus, the blocking diode prevents the discharging of battery into the SPV module. The connection of blocking diode with a solar PV module is shown in Figure 4.23.

How to identify diode ?

The diode by appearance is cylindrical in shape with a silver ring on it, and other part is black in colour. The diode has two pins; one is positive and other one is negative. The silver ring (as shown in Figure 4.24) represents the negative terminal and other terminal is positive.

Typical diode ratings

The diodes used for bypass and blocking are different modules / cells depending on their current and voltage ratings. There are various ratings of diodes available. The ratings of a bypass diode, which is used for 16-19 cells in series, is the total current flowing through the series connected cells in a string. That means, the one module of 36 cells contains 2 bypass diodes and a module with 72 cells contains 4 bypass diodes. Typically, the rating of bypass diode is of order 5-10 ampere and 30-50 volts (depending on the number of cells which are connected in series and their current and voltages. The blocking diode ratings depend on the array current and the voltage because main function of these diodes is to block the current coming from the battery during night when modules do not produce any power. Typical ratings of the blocking diode ranges from small current like 10s of ampere to the large current like 100s ampere for SPV arrays.