# Series, Parallel & Series-Parallel Connection of Solar Panels

**Series, Parallel and Series-Parallel Configuration of Photovoltaic Arrays**

**What is a Solar Photovoltaic Array?**

A Solar Photovoltaic Module is available in a range of 3 W_{P} to 300 W_{P}. But many times, we need power in a range from kW to MW. To achieve such a large power, we need to connect N-number of modules in series and parallel.

**A String of PV Modules**

When N-number of PV modules are connected in series. The entire string of series-connected modules is known as the PV module string. The modules are connected in series to increase the voltage in the system. The following figure shows a schematic of series, parallel and series parallel connected PV modules.

**PV Module Array**

To increase the current N-number of PV modules are connected in parallel. Such a connection of modules in a series and parallel combination is known as “Solar Photovoltaic Array” or “PV Module Array”. A schematic of a solar PV module array connected in series-parallel configuration is shown in figure below.

**Solar Module Cell:**

The solar cell is a two-terminal device. One is positive (anode) and the other is negative (cathode). A solar cell arrangement is known as solar module or solar panel where solar panel arrangement is known as photovoltaic array.

It is important to note that with the increase in series and parallel connection of modules the power of the modules also gets added.

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**Series Connection of Modules**

Sometimes the system voltage required for a power plant is much higher than what a single PV module can produce. In such cases, N-number of PV modules is connected in series to deliver the required voltage level. This series connection of the PV modules is similar to that of the connections of N-number of cells in a module to obtain the required voltage level. The following figure shows PV panels connected in series configuration.

With this series connection, not only the voltage but also the power generated by the module also increases. To achieve this the negative terminal of one module is connected to the positive terminal of the other module.

If a module has an open circuit voltage V_{OC1 }of 20 V and other connected in series has V_{OC2 }of 20 V, then the total open circuit of the string is the summation of two voltages

**V _{OC} = V_{OC1 }+ V_{OC2}**

V_{OC} = 20 V + 20 V = **40 V**

It is important to note that the summation of voltages at the maximum power point is also applicable in case of PV array.

**Calculation of the Number of Modules Required in Series and their Total Power**

To calculate the number of PV modules to be connected in series, the required voltage of the PV array should be given. We will also see the total power generated by the PV array. Note that all the modules are identical having the same module parameters.

**Step 1:** Note the voltage requirement of the PV array

Since we have to connect N-number of modules in series we must know the required voltage from the PV array

- PV array open-circuit voltage V
_{OCA} - PV array voltage at maximum power point V
_{MA}

**Step 2:** Note the parameters of PV module that is to be connected in the series string

PV module parameters like current and voltage at maximum power point and other parameters like V_{OC}, I_{SC,} and P_{M} should also be noted.

**Step 3:** Calculate the number of modules to be connected in series

To calculate the number of modules “N” the total array voltage is divided by voltage of individual module, Since the PV module is supposed to be working under STC the ratio of array voltage at maximum power point V_{MA} to module voltage at maximum power point V_{M} is taken.

A similar calculation for open-circuit voltage of PV can also be done i.e. ratio of array voltage at open circuit V_{OCA} to module voltage at open circuit V_{OC}. Note that the value of “N” can be a non-integer so we have to take next higher integer and so the value of V_{MA} and V_{OCA} will also increase than what we desired.

**Step 4:** Calculating the total power of the PV array

The total power of the PV array is the summation of the maximum power of the individual modules connected in series. If P_{M} is the maximum power of a single module and “N” is the number of modules connected in series, then the total power of the PV array P_{MA} is N × P_{M}.

We can also calculate the array power by the product of PV array voltage and current at maximum power point i.e.

**V _{MA} × I_{MA}**

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**Example:**

Now to understand these steps in a more mathematical way. Let’s take an example of a power plant of 2 MW, in which a large number of PV modules are connected in series. The 2 MW inverter can take input voltage from 600 V to 900 V.

Determine the number of modules be connected in series to obtain a maximum power point voltage of 800 V. Also determine the power delivered by this PV array. The parameters of the single PV module are as follows;

- Open circuit voltage V
_{OC}= 35 V - Voltage at maximum power point V
_{M}= 29 V - Short circuit current I
_{SC}= 7.2 A - Current at maximum power point I
_{M}= 6.4 A

**Step 1:** Note the voltage requirement of the PV array

- PV array open-circuit voltage V
_{OCA}= Not given - PV array voltage at maximum power point V
_{MA}= 800 V

**Step 2:** Note the parameters of PV module that is to be connected in the series string

Open circuit voltage V_{OC} = 35 V

Voltage at maximum power point V_{M} = 29 V

Short circuit current I_{SC} = 7.2 A

Current at maximum power point I_{M} = 6.4 A

Maximum Power P_{M}

**P _{M} = V_{M} x I_{M}**

= 29 V x 6.4 A

**P _{M} = 185.6 W**

**Step 3:** Calculate the number of modules to be connected in series

**N = V _{MA} / V_{M} **

N = 800 / 29

**N = 27.58** (Higher integer value 28)

Take higher integer value 28 modules. Due to the higher integer value of N, the value of V_{MA} and V_{OCA} will also increase.

V_{MA} = V_{M} × N

= 29 × 28

**= 812 V**

**Step 4:** Calculating the total power of the PV array

**P _{MA} = N × P_{M}**

= 28 × 185.6

**= 5196.8 W**

Thus, **we need 28 PV modules to be connected in series** **having a total power of 5196.8 W to obtain the desired maximum PV array voltage of 800 V.**

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**Mismatch in Series-connected PV Modules**

The maximum power in the PV module is the product of voltage and current at maximum power. When the modules are not connected in series then the power produced by an individual module is different. Take the example of table 1 given below.

Table 1

Modules | V_{M }in Volts | I_{M }in Ampere | P_{M} in Watt |

Module A | 16 | 4.1 | 65.6 |

Module B | 15.5 | 4.1 | 63.55 |

Module C | 15.3 | 4.1 | 62.73 |

Total | In series = 46.8 | In series = 4.1 | 191.88 |

If the three modules in table 1 are connected in series their voltage is added but the current remains the same considering all the modules are identical having the same value of I_{M} = 4.1 A.

The difference in the voltages of the modules A, B, and C connected in series does not result in the loss of the power produced by the PV module array considering all the modules are identical having the same value of I_{M} = 4.1 A.

But if the current producing capacity of the modules connected in series is not identical then the current flowing through the series-connected PV modules will be equal to the lowest current produced by a module in the string. Take an example table 2 given below.

Table 2

Modules | V_{M }in Volts | I_{M }in Ampere | P_{M} in Watt |

Module A | 16 | 4.1 | 65.6 |

Module B | 15.5 | 3.2 | 49.6 |

Module C | 15.3 | 4.1 | 62.73 |

Total | In Series = 46.8 | In Series = 3.2 | 177.93 |

If all the modules in table 2 are connected in series then the current flowing through the series-connected modules is determined by the module with the lowest current. In this case module B has the lowest current of 3.2 A as compared to modules A and C.

So, the current flowing through these three series-connected modules is 3.2 A. Now compare Tables 1 and 2 and the total power produced by both. Due to unidentical current modules in table 2 the total power produced is 177.93 W which is less than the total power produced by modules in table 1 i.e. 191.88 W.

We can see that due to the mismatch in current the output power produced by the series-connected modules is widely affected. So, in the series connection of modules mismatch in voltage is not an issue but mismatch in current results in loss of power. Hence modules with different current ratings should not be connected in series.

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**Parallel Connection of Modules**

Sometimes to increase the power of the solar PV system, instead of increasing the voltage by connecting modules in series the current is increased by connecting modules in parallel. The current in the parallel combination of the PV modules array is the sum of individual currents of the modules.

The voltage in the parallel combination of the modules remains the same as that of the individual voltage of the module considering that all the modules have identical voltage.

The parallel combination is achieved by connecting the positive terminal of one module to the positive terminal of the next module and negative terminal to the negative terminal of the next module as shown in the following figure. The following figure shows solar panels connected in parallel configuration.

If the current I_{M1} is the maximum power point current of one module and I_{M2 }is the maximum power point current of other module then the total current of the parallel-connected module will be I_{M1 }+ I_{M2}. If we keep on adding modules in parallel the current keeps adding up. It is also applicable for short-circuit current Isc.

**Calculation of the Number of Modules Required in Parallel and their Total Power**

To calculate the number of PV modules to be connected in parallel, the required current of the PV array should be given. We will also see the total power generated by the PV array. Note that all the modules are identical having the same module parameters.

**Step 1:** Note the current requirement of the PV array

Since we have to connect N-number of modules in parallel we must know the required current from the PV array

- PV array short-circuit current I
_{SCA} - PV array current at maximum power point I
_{MA}

**Step 2:** Note the parameters of PV module that is to be connected in parallel

PV module parameters like current and voltage at maximum power point and other parameters like V_{OC}, I_{SC,} and P_{M} should also be noted.

**Step 3:** Calculate the number of modules to be connected in parallel

To calculate the number of modules N the total array current is divided by the current of an individual module, Since the PV module is supposed to be working under STC the ratio of array current at maximum power point I_{MA} to module current at maximum power point I_{M} is taken.

A similar calculation for short-circuit current of PV can also be done i.e. ratio of array short-circuit current I_{SCA} to module short-circuit current I_{SC}.

Note that the value of N can be a non-integer so we have to take next higher integer and so the value of I_{MA} and I_{SCA} will also increase than what we desired.

**Step 4:** Calculating the total power of the PV array

The total power of the PV array is the summation of the maximum power of the individual modules connected in parallel. If P_{M} is the maximum power of a single module and “N” is the number of modules connected in parallel, then the total power of the PV array P_{MA} is N × P_{M}. we can also calculate the array power by the product of PV array voltage and current at maximum power point i.e. V_{MA} × I_{MA}.

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**Example:**

Let’s take an example, calculate the number of modules required in parallel to obtain maximum power point current I_{MA }of 40 A. The system voltage requirement is 14 V. The parameters of the single PV module are as follows;

- Open circuit voltage V
_{OC}= 18 V - Voltage at maximum power point V
_{M}= 14 V - Short circuit current I
_{SC}= 6.5 A - Current at maximum power point I
_{M}= 6 A

**Step 1:** Note the current requirement of the PV array

- PV array short-circuit current I
_{SCA}= Not given - PV array current at maximum power point I
_{MA}= 40 A

**Step 2:** Note the parameters of PV module that is to be connected in parallel

Open circuit voltage V_{OC} = 18 V

Voltage at maximum power point V_{M} = 14 V

Short circuit current I_{SC} = 6.5 A

Current at maximum power point I_{M} = 6 A

Maximum Power:

** P _{M} = V_{M} x I_{M}**

P_{M} = 14V x 6A

**P _{M} = 84 W**

**Step 3:** Calculate the number of modules to be connected in parallel

N = I_{MA} / I_{M}

= 40 / 6

N = 6.66 (Higher integer value 7)

Take higher integer value 7 modules. Due to the higher integer value of N, the value of I_{MA} and I_{SCA} will also increase.

**I _{MA }= I_{M} × N**

= 6 × 7

**I _{MA} = 42 A**

Step 4: Calculating the total power of the PV array

**P _{MA} = N × P_{M}**

= 7 × 84

**P _{MA} = 588 W**

Thus, we need 7 PV modules to be connected in parallel having a total power of 588 W to obtain the desired maximum PV array current of 40 A.

**Mismatch in Parallel-connected PV Modules**

In a parallel connection, the issue of mismatch in current is not a problem but the mismatch in voltage is a problem. In parallel-connected modules, the voltage will remain the same if the modules have identical voltage ratings.

But if the voltage rating of parallel-connected modules is different then the system voltage is determined by the module having the lowest voltage rating resulting in the power loss.

The effect of voltage mismatch is not as severe as the current mismatch but care must be taken while choosing the modules. It is recommended that for series combination modules of the same current rating and for parallel combination modules of the same voltage rating should be preferred.

### Series – Parallel Connection of Modules – **Mixed Combination**

When we need to generate large power in a range of Giga-watts for large PV system plants we need to connect modules in series and parallel. In large PV plants first, the modules are connected in series known as “PV module string” to obtain the required voltage level.

Then many such strings are connected in parallel to obtain the required current level for the system. The following figures shows the connection of modules in series and parallel. To simplify this, take a look at right in the following figure.

Module 1 and module 2 are connected in series let’s call it the string 1. The open-circuit voltage of the string 1 V_{OC1} is added i.e.

**V _{OC1} = V_{OC} + V_{OC} = 2V_{OC}**

Whereas the short-circuit current of string 1 I_{SC1} is the same i.e.

**I _{SC1} = I_{SC}**

Similar to string 1, the modules 3 and 4 make up the string 2. The open-circuit voltage of the string 2 V_{OC2} is added i.e.

**V _{OC2} = V_{OC} + V_{OC} = 2V_{OC}**

Whereas the short-circuit current of string 2 I_{SC2} is the same i.e.

**I _{SC2} = I_{SC}**

Now string 1 and string 2 are connected in parallel, nowhere the voltage remains the same but the current is added i.e. open-circuit voltage of the PV module array

**V _{OCA} = V_{OC1} = V_{OC2} = 2V_{OC}**

And Short circuit current of the PV module array

**I _{SCA} = I_{SC1} + I_{SC2} = I_{SC} + I_{SC} = 2I_{SC}**

The same calculation is applicable for voltage and current at the maximum PowerPoint.

**Calculation of the Number of Modules Required in Series – Parallel, and their Total Power**

Here for the calculation of the number of modules required in series and parallel, and power we have assumed that all the modules have identical parameters. Note that;

- N
_{S}= Number of modules in series - N
_{P}= Number of modules in parallel

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

- PV array power P
_{MA} - PV array voltage at maximum power point V
_{MA} - PV array current at maximum power point I
_{MA}

**Step 2:** Note the PV module parameters

PV module parameters like current and voltage at maximum power point and other parameters like V_{OC}, I_{SC,} and P_{M} should also be noted.

**Step 3:** Calculate the number of modules to be connected in series and parallel

To calculate the number of modules in series N_{s} the total array voltage is divided by the voltage of an individual module, Since the PV module is supposed to be working under STC the ratio of array voltage at maximum power point V_{MA} to module voltage at maximum power point V_{M} is taken.

Similarly, to calculate the number of modules in parallel N_{p} the total array current is divided by the current of an individual module, Since the PV module is supposed to be working under STC the ratio of array current at maximum power point I_{MA} to module current at maximum power point I_{M} is taken.

Similar calculations for open-circuit voltage and short-circuit current can be done. Note that the value of N_{s }and N_{P} can be a non-integer so we have to take next higher integer and so the value of I_{MA}, I_{SCA}, V_{MA}, and V_{OCA} will also increase than what we desired.

**Step 4:** Calculating the total power of the PV array

The total power of the PV array is the summation of the maximum power of the individual modules connected in series and parallel.

If P_{M} is the maximum power of a single module, and N_{S} is the number of modules connected in series and N_{P} is the number of modules connected in parallel, then the total power of the PV array

**P _{MA} = N_{P} × N_{S }× P_{M}**

We can also calculate the array power by the product of PV array voltage and current at maximum power point i.e.

V_{MA} × I_{MA}

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**Example:**

Now let’s take an example for the mix – combination. We have to determine the number of modules required for a PV array having the following parameters;

- Array power P
_{MA}= 40 KW - Voltage at maximum power point of array V
_{MA}= 400 V - Current at maximum power point of array I
_{MA}= 100 A - The module for the design of the array has the following parameters;
- Voltage at maximum power point of module V
_{M}= 70 V - Current at maximum power point of module I
_{M}=17 A

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

- PV array power P
_{MA}= 40 KW - PV array voltage at maximum power point V
_{MA}= 400 V - PV array current at maximum power point I
_{MA}= 100 A

**Step 2:** Note the PV module parameters

Voltage at maximum power point of module V_{M} = 70 V

Current at maximum power point of module I_{M} = 17 A

Maximum power P_{M}:

**P _{M} = V_{M} x I_{M}**

P_{M} = 70V x 17A

**P _{M} = 1190 W**

**Step 3:** Calculate the number of modules to be connected in series and parallel

N_{S} = V_{MA} / V_{M}

N_{S }= 400 / 70

N_{S }= 5.71 (Higher integer value 6)

Take higher integer value 6 modules. Due to the higher integer value of N_{S}, the value of V_{MA} and V_{OCA} will also increase.

**V _{MA} = V_{M} × N_{S}**

= 70 × 6

**V _{MA} = 420 V**

Now,

N_{P} = I_{MA} / I_{M}

N_{P} = 100 / 17

N_{P} = 5.88 (Higher integer value 6)

Take higher integer value 6 modules. Due to the higher integer value of N_{P}, the value of I_{MA} and I_{SCA} will also increase.

I_{MA} = I_{M} × N_{P}

I_{MA} = 17 × 6

**I _{MA} = 102 A**

**Step 4:** Calculating the total power of the PV array

**P _{MA} = N_{S} × N_{P} × P_{M}**

= 6 × 6 × 1190

**P _{MA} = 42840 W**

Thus, **we need 36 PV modules**. A string of six modules connected in series and six such strings connected in parallel, having a total power of 42840 W to obtain the desired maximum PV array current of 100 A and voltage of 400 V.

Note that due to higher integer value of 6 the maximum PV array current and voltage is 102 A and 420 V respectively.

**Conclusion**

In this article, an in-depth study of the solar photovoltaic module and array was carried out. The need, structure, and design of the modules for higher power level was studied. It also included a procedure for parameter measurement and explanation of bypass diode and blocking diode for the safety of the module.

We also saw an explanation of the PV module array along with its need and connection combination. Calculation and procedure for the design of series, parallel, and mix connections were done in detail along with the study of mismatch in voltage and current of the modules. Such a study of Photovoltaic module and array is a must requirement for a designer of the PV system.

The article gives a significant design understanding of important components (modules and array) in the PV system, which can be utilized to make a proper, efficient, and reliable design in a PV system.

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