# String and Array sizing for a solar project

When number of modules are connected in series and parallel combination it is known as PV array and the effective output of a PV array is determined based on the parallel/series combination of PV modules. Typically, PV array is sized based on inverter input voltage considerations. In case of a typical 1000 V_{DC} inverter voltage, a string is formed by connecting about 20 modules in series.

In recent years the inverters are available with a 1500 V_{DC} inverter voltage and string sizing is done by connecting about 28 or 30 modules in series.

Before we dive into the steps to calculate a string and an array let us understand some terminologies: –

**Series – **The connection of modules which gives us added voltage though the current remains same.

**Parallel – **The connection of modules which gives us added current though the voltage remains same.

**String – **The connection of modules in series formation is termed as string. We can also say number of modules connected in series in a string.

**Array – **The connection of modules in parallel formation is called an array. We also say this as total number of strings that forms an array.

**Maximum Power Point Tracking (MPPT) – **The maximum power at a particular voltage and current level.

__Sizing an array: –__

Step I

Calculate maximum open circuit voltage (V_{OC}) of module at minimum temperature by the formula: –

V_{min temp} = V_{OC} [1 + β (Temperature difference)]

Where,

β = Temperature co-efficient of voltage

Temperature difference = T_{2} – T_{1}

T_{2} = Assumed temperature (here minimum temperature)

T_{1 }=Temperature at STC (i.e., 25^{o}C)

Step II

Now calculate maximum number of modules in a string by the formula: –

= Maximum V_{DC} of Inverter / V_{min temp}

Step III

Now calculate total number of strings by the formula: –

= Total modules required / modules in a string

After that we have calculated and sized our modules per string and number of strings, we need to cross verify and check that our calculations are under the permissible limits. Following is the checklist to be carried out: –

- Check for maximum strings that can be connected to the inverter by the formula: –

No. of independent MPP inputs × Max. number of input connector per MPPT.

2. Check for maximum pv input current.

3. Check for maximum DC short-circuit current.

__Let us take an example: –__

DC capacity – 500 kW_{p}

Inverter of 250 kVA

Modules wattage – 540 W_{p }(.54 kW_{p})

Step I

Calculate total modules required

= DC capacity / Wattage of each module

= 500 / .54

= 925.92

~ 925 modules

Step I

Calculate maximum open circuit voltage (V_{OC}) of module at minimum temperature (we have assumed here to be 10^{°}C) by the formula: –

V_{min temp} = V_{OC} [1 + β (Temperature difference)]

V_{10°C} = 49.42 [1 + (- 0.28%) (T_{2} – T_{1})]

V_{10°C} = 49.42 [1 + (- 0.0028) (10 – 25)]

V_{10°C} = 49.42 [1 + (- 0.0028) (- 15)]

V_{10°C} = 49.42 [1 + (0.042)]

V_{10°C} = 49.42 [1.042]

V_{10°C} = 51.49 V

Step II

Now calculate maximum number of modules in a string by the formula: –

= Maximum V_{DC} of Inverter / V_{10°C}

= 1500 / 51.49

= 29.13

~ 29 modules in a string

Step III

Calculate total number of strings by the formula: –

= Total modules required / modules in a string

= 925 / 29

= 31.89

~ 31

As the article earlier explained to carry a checklist to cross verify our calculations. Following is the checklist to be carried out: –

- Check for maximum strings that can be connected to the inverter by the formula: –

No. of independent MPP inputs × Max. number of input connector per MPPT

12 × 2 = 24

Please note here that we have only 24 inputs to be connected in the inverter but as per our calculations we have 31 strings. Now to connect these 31 strings keeping in mind the limitation of the inverter, we can use “Y Connector”. So,

30 / 2 = 15

15 + 1 (left-over string) = 16

So, here we have used “Y Connectors” with 30 strings (to make our calculations easy) and we will add the left-over string with result. Thus, the calculated value is 16 total inputs to be connected and spared is 24 – 16 = 8 inputs.

2. Check for maximum pv input current from the inverter datasheet.

30 Amps × 12 = 360 Amps (value of current at maximum power that the inverter can tolerate)

I_{MP }× total inputs used in an inverter

= 13.27 Amps × 16

= 212.32 Amps

= 212.32 Amps ˂ 360 Amps (check verified)

3. Check for maximum DC short-circuit current.

50 Amps × 12 = 600 Amps (maximum value of current at zero voltage that the inverter can tolerate)

I_{SC }× total inputs used in an inverter

= 13.85 Amps × 16

= 221.6 Amps

= 221.6 Amps ˂ 600 Amps (check verified)

I-V characteristics curve of a string and an array for a 1500 V_{DC} system is shown in following figure (notice the MPPT levels in both the curves, also notice that the MPPT level has increased in the array I-V curve): –