String size calculation in Grid tied Solar PV system

Solar modules are connected in series or parallel or series-parallel combination to get the required voltage, current and power. Series connection will increase the string voltage while keeping the current constant. On the other hand parallel connection will increase the current whereas the voltage remains the same. Now what about the voltage, current and power in the series-parallel connection? Yes  you are correct, all the three will increase.

The capacity of the solar PV plant depends on the roof space available and the individual requirement. Once the PV module capacity is decided we can size the inverter. Normally the inverter size is smaller than the rated output of the PV array at Standard Test Conditions (STC). This is due to the losses or de-rating factors such as panel dissimilarity, dust, losses in cables etc. An inverter of 80 % size of the PV array is quite normal.  

What is a string in the solar PV system?

Number of modules connected in series is called the “string”. Size of the string determines the voltage input to the inverter. The maximum and minimum number of modules in the string depends on the maximum and minimum voltage of the inverter.

The output voltage generated from the PV should never damage the inverter that’s why we have to calculate the maximum system voltage. The maximum system voltage should not be more than the highest acceptable inverter voltage.

Similarly we have to calculate the minimum number of modules in the string so that in worst case scenario the PV system’s output voltage is sufficient enough to turn the inverter ‘ON’.

Relationship between Ambient Temperature and String Output:

As expected, a certain relation exists between the ambient temperature and the string voltage, which is to be considered while calculating or designing the string size.  The PV output is inverse to the ambient temperature i.e. with the decrease in ambient temperature; there is a certain increase in string voltage and power. The vice-versa happens during summer season. With a correctly sized PV array, the DC output will remain within the optimum operating range of the inverter under different working and ambient conditions.

What should be the minimum string size in the solar PV system?

Softwares are also used in the design, construction, operation and maintenance of Solar PV plants. These softwares help to optimize the design configuration and system layouts.

In the following paragraphs, manual calculations of string size is given for the easy understanding of concepts. They are easy enough to be done manually.

For the calculation we need some data from the data-sheet of the module. Suppose the;

Voltage at Open Circuit, V_OC = 43.4 V,

Temperature at Standard Test Condition (STC) = 25^oC,

Temperature Coefficient at V_OC = (-) 0.15 V/ ^oC,

Voltage at Maximum Power, V_mp = 35.4 V,

Temperature Coefficient at V_mp = (-) 0.17 V/ ^oC,

Now from the inverter data sheet, we have to get the maximum input DC voltage and the start ( or strike) voltage of the inverter. From the environmental data we have to collect the hottest day-time temperature and coldest day-time temperature of the location where the PV system is to be installed.

Suppose that the effective cell temperature during the hottest day is 70 ^oC, which is 45 ^oC above the temperature at Standard Test Condition (STC) of 25^oC.

Therefore, the V_mp voltage would be changed (reduced) by 45 x (-) 0.17 = (-) 7.65 V

Hence the V_mp at 70 ^oC cell temperature would be 35.4 + (– 7.65) = 27.75 V.

Next we should consider the de-rating factor which is due to the earlier mentioned factors such as module mismatch, dust & dirt, cable loss etc. Let it be 0.88.

So the effective minimum V_mp for each module at the inverter input would be 27.75 x 0.88 = 24.4 V.

From the above results we can calculate the minimum permissible number of modules in the string.

Assume that the minimum start (or strike) voltage for the inverter is 140 V. Taking a safety margin of 10%, i.e. 140 x 1.1 = 154 V. This means that the string size should be so selected that a minimum of 154 V is maintained at the inverter input terminals in the worst case scenario.

Hence the minimum number of modules in the string to surpass the start voltage is

154/ 24.4 =  6.31 rounded up to 7 modules.

What should be the maximum string size in the solar PV system?

As mentioned earlier, the output voltage of a solar PV module increases as the ambient temperature drops below the temperature at STC.  At the coldest day-time temperature the V_OC of the array shall never be greater than the maximum allowed input voltage of the inverter. Now we have to calculate the maximum number of modules in the string. Oversizing the string can damage the inverter, cancel warranties and violate the safety codes.

Let’s suppose that during the coldest day, the effective cell temperature is 15 ^oC, which is 10 ^oC below the temperature at STC of 25^oC. 

Therefore the V_OC should be increased by (15 – 25) x (-) 0.15 = 1.5 V. You can say that the Voc at 15 ^oC is 43.4 + 1.5 = 44.9 V.

Assume that the maximum safe working voltage allowed by the inverter is 400 V. Then the maximum number of modules permissible in the string is 400/ 44.9 = 8.9 rounded down to 8 modules.

The goal of this article was to convey the basic process for sizing the PV string for a grid connected system. Let’s promote Solar PV system in our vicinity.