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# Chapter number 3.0 Solar Cells, Modules & Arrays

- March 29, 2023
- Posted by: iisemumbai
- Category: Learning Resources

A single solar cell does not produce enough power (voltage and current) to operate the load and, therefore, many cells are connected together to make a PV module. The PV modules are available in wattage rating of 3 Wp to 300 Wp. A PV module is characterized by several parameters including *I*sc, *V**o*c,* I*m, *V*m, *W*p, (*P*max or *P*m), FF and *ɳ*. The main parameter useful for the practical applications are *I*m, *V*m and *P*m. While showing a large number of modules, a representative symbol of module is used.

Many times, in practice, we need power in large quantity, like in several hundred watts, kW and in MW. In order to have a large power generations (larger than a single PV module can produce), these solar PV modules are connected in series and/or parallel combinations.

*PV module string: *

When many PV modules are connected in series, a single row of series connected PV modules is referred as PV module string. The series connection of PV modules is used for increasing the voltage in PV systems. A schematic representation of series connected PV modules or a PV module string.

*PV modules array : *

In order to increase the current in PV system, the PV individual PV modules or PV module strings are connected in parallel. Such series and parallel combination of PV modules is referred as ‘solar PV array’.

A schematic diagram of a solar PV array and a photograph of a installed solar PV array is shown in Figure 5.4. When the number of modules are connected in series and/or parallel combination, the symbol of PV module can be used for the representation of the modules. Note that, in both series and parallel combination of PV modules, the power of the PV modules always gets added.

In order to get power output larger than a single PV module can generate, many PV modules are connected in series and/or parallel in the form of PV array.

**5.1**** Connection of Modules in Series**

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 the output voltage of a PV module up to certain level, for instance, up to 15V at maximum power point. Normally, the standard maximum voltages of module are 15V, 30V and 45V. 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 connection of PV modules, it is not only the PV module voltage that increases but 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. The negative terminal of one module is connected with the positive terminal of the other module. When two modules with open circuit voltage of *V*oc1 and *V*oc2 are connected in series, the voltage of series combination is the addition of two voltages, which is *V*oc1 + *V*oc2 . 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 *V*m, the voltage at maximum power point. An example of two PV modules with series connection is given in Table 5.1.

When PV modules are connected in series, the voltage of the series connected PV modules is the sum of the voltages of individual PV modules.

In the same way the voltage at maximum power point , *V*m of the PV modules can also be added.

When three modules with open circuit voltage of *V*oc1 *V*oc2 and *V*oc3 are connected in series, the total voltage of series combination will be the sum of these three voltages, i.e.* V*oc1 + *V*oc2 + *V*oc3.

**5.1.1 Estimating Number of PV Modules Required in Series and Their Total Power**

It is mentioned in the earlier sections that PV modules are connected in series in 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, then we can call the series connection of PV modules as ‘PV modules array’ in 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 *V**o*c,* I*sc* , V*m, and *I*m .

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 :

**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 ,* V*m, and *I*m of the available PV module (or PV module specified by client) must be noted. Other PV module information like *V**o*c,* I*sc* ,* and *P*m can also be noted in the following table :

**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 *V*ma to *V*m (array module voltage to module voltage at maximum power point) should be taken as follows:

If the ratio of *V*ma to *V*m is not an integer, then the next integer value should be taken. For instance, if the ratio is 3.5. We know that number of modules cannot be 3.5, it can be either 3 or 4. Therefore, in this case, the next integer number, i.e., 4 should be taken.

Also note in the above table that the current at maximum power point of PV array remains the same as that of current of individual PV module, i.e.* I*ma = *I*m.

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 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 *N*s PV modules are connected in series and maximum power of one PV module is *P*m, then the total power output of the PV array (*P*ma) would be *N*s X *P*m . 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, *V*ma and *I*ma. The PV module array power is the product of *V*ma and *I*ma , that is, *P*ma = *V*ma X *I*ma.

**5.1.2 Mismatch in Voltage in Series Connected PV Modules**

Maximum power or the peak power output of a PV module (under STC) is the product of current at maximum power point (*I*m) and voltage at maximum power point (*V*m). When PV modules are not connected with each other, the total peak power produced by PV modules is the sum of the total peak power produced by individual modules. An example of total power produced by three individual PV modules is given in Table 5.4.

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 *I*m of 5.1 A each. Therefore, the current when three modules are connected in series will be 5.1A. An example of calculation of *P*m of three series connected PV modules is given in Table 5.5. Compare the total power output of three individual PV modules. One can notice that the difference in *V*m 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 output of series connected PV modules.

The difference in the voltages of series connected PV modules does not affect the total power generating capacity of the combination.

**5.1.3 Mismatch in Current in Series Connected PV Modules**

In series connection, only voltage gets added but current remains the same, provided 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 modules will be equal to the current of the module with the lowest current producing module determines the current in series connected modules. For examples, if there are three modules having *I*m of 5.1A, 4.9A and 5.0A, then the current of the series combination of these modules will be 4.9A (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 capacity of three individual module 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 *I*m should not be connected in series.

PV modules with difference in *I*m should not be connected in series. It results in loss of power output.

**5.2**** Connection of Modules in Parallel Combination**

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 PV modules is discussed in Section 5.1. Sometimes, instead of series 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.

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 *I*sc1 and *I*sc2 , then the total current of parallel connection will be = *I*sc1 + *I*sc2. 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 2A current is given in Table 5.7. The above description is given for short circuit current, but it is applicable for any other current component of PV modules. Thus, if current at maximum power point of two PV modules is *I*m1 and *I*m2, then the total current at maximum power point of parallel connection will be *I*m1 + *I*m2.

In parallel combination of PV modules, currents get added while the voltage of combination remains the same as that of a single PV module.

**5.2.1 Power Generated by Parallel Connected PV Modules**

The *P*m of a PV module (under STC) is the product of current at maximum power point (*I*m) and voltage at maximum power point *(V*m). When PV modules are not connected with each other, the total peak power produced by the PV modules is the sure of the peak power produced by individual modules. An example of total power produced by three individual PV modules (having same *V*m but different *I*m). The total power produced by three individual PV modules is 255 watt. When these modules are connected in parallel, the *V*m of the parallel combination is same as *V*m of individual PV modules which is 17 V. Now, the total *I*m of the parallel combination will be the sum of *I*m of each PV modules, which is 15A. 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.

**5.2.2** **Estimating the Number of PV Modules to be Connected in Parallel and Their Total Power**

When PV modules are connected in parallel, the current of individual PV module 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 combination. In a PV array, either individual PV modules can be connected in 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 *V**o*c,* I*sc* , V*m, and *I*m . 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.

**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 condition, therefore, current and voltage at maximum power point, that is *V*m and *I*m of available PV module or PV module strings must be noted. Other PV module information’s like *V**o*c,* I*sc and *P*m can also be noted.

**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 (*I*ma) is divided by the current of individual modules or module string (*I*ma). Since in real time, PV modules are supposed to work under maximum power point condition, the ratio of *I*ma to *I*m (PV array current to module current at maximum power point)

If the ratio of *I*ma to *I*m 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.

In parallel connection, the voltage of the PV array, remains the same as that of voltage of individual PV module or PV module string. Therefore, note here, in the above table that the voltage at maximum power point of PV array remains same as that of voltage of individual PV module or module string, i.e. *V*ma = *V*m.

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 module strings. Thus, if *N*p PV modules or strings are connected in parallel and maximum power of one PV module or strings is *P*m, then the total power output of the PV array is *P*ma = *N*p X* P*m . The PV array power output can also be calculated from PV array voltage and current at maximum power point, that is *V*ma and *I*ma. The PV module array power is the product of *V*ma and *I*ma, that is, *P*ma = *V*ma X *I*ma. This can be tabulated in the following way:

**5.2.3 Mismatch in Module Voltages Connected in Parallel**

It has been mentioned that the voltage of parallel combination of PV modules is 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 determined by the PV module with lowest voltage. Normally, the effect of difference in modules voltages in parallel 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 PV modules of different power ratings together, effort should be made to put PV modules of same current rating in series combination and PV modules of same voltage ratings in parallel combination.

**5.3 ****Connection of Modules in Series and Parallel **(Mixed Combination)** **

When the PV power requirement is more than few hundred watts, the PV module needs to be connected in both series and in parallel combination. Also, when we need to generate a very large amount of power, like in solar PV megawatt scale power plants, then the PV modules are connected in both series and parallel configuration 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.

In this example, four identical PV modules (Module 1, Module 2, Module 3 and Module 4) with open circuit voltage of *V*oc and short circuit current of *I*sc are used.

In Figure 5.15, the connection of four identical PV modules is shown, each PV module having short circuit current of *I*sc and open circuit voltage of *V*oc. 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 voltage remains the same. In this case, Module 1 and Module 2 are connected in series, let us call it string 1. Similarly, Module 3 and Module 4 are also connected in series, let us call it string 2. Since all the PV modules are identical, the open circuit voltage of string 1 (*V*oc 1) and short circuit current of PV module string 1 (*I*sc 1) will be 2 X *V*oc and *I*sc respectively. Similarly, the open circuit voltage of PV module string 2 will be 2 X *V*oc while the short circuit current will be *I*sc.

Now, the PV module string 1 and string 2 are connected in parallel (this combination of series and parallel PV module 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 (*V*oc1 = 2* V*oc, and *V*oc2 = 2*V*oc), the open circuit voltage of the PV module array, *V*ocr =* V*oc1 =* V*oc2 =2*V*oc. The short circuit current of string 1 is *I*sc1 = *I*sc and that of string 2 is *I*sc2 = *I*sc. Therefore the short circuit current of PV module array, *I*scr, wherein two strings are connected in parallel is *I*sc1 + *I*sc2 +* I*sc +* I*sc = 2*I*sc. In this case of PV module array, the array open circuit voltage will be 2* V*oc and the array short circuit current will be 2*I*sc.

In the same way, current and voltage of any combination of series and parallel connected PV modules can be obtained. In practice, PV modules do not operate at open circuit and short circuit conditions, but they operate under maximum power point condition. Therefore, for calculations, current at maximum power point (Vm) should be taken for calculations.

**5.3.1 Estimation Number of Modules to be Connected in Series and Parallel and their Total Power**

The objective of making series and parallel combination of PV modules, to form 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 module string) to get higher voltages and modules are connected in series (to form module string) to get higher voltages and modules or module strings are connected in parallel to get higher currents. In both series and parallel combination, the 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 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 *V*oc ,Vm, *I*sc and *I*m. 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, *P*ma should be noted. If the desired current of array (*I*ma) and desired voltage of array (*V*ma) 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 *P*ma = *I*ma X *V*ma relationship. All three parameters ; power, voltage and current are assumed at maximum power point condition.

**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 *V*m and *I*m of a PV module to be connected in PV array, must be noted. Other PV modules information like *V*oc , *I*sc and *P*m can also be noted.

**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.

The value of *N*s and *N*p should be an integer. If the calculated ratio is not an integer, then the next higher integer value should be chosen. Thus, if *N*s 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 *N*p 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 *N*s PV modules are connected in series and *N*p such series are connected in parallel, then the total number of PV modules connected in PV arrays is *N*s X *N*p . Now, if maximum power of one PV module is *P*m then the total power output of the PV array (*P*ma) would be *N*s X *N*p X *P*m. 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 & current at maximum power point, that is *V*m and *I*m. The PV module array power is the product of *V*m and *I*m and *P*ma = *I*ma X *V*ma.