How to size the battery for your solar power system?

26/2/2015

If you are going for off- grid solar power system then there should be a back up support to provide electricity during night or when sun light is less. Here comes the role of the battery, an ideal sizing of the battery as per your needs can solve your problem.

The sizing of the battery depends on:

Amount of the load
How many hours the load is to be run?
Depth of discharge of the battery
Efficiency of the battery
Efficiency of the inverter

(1) Calculating the total load

Let us understand all this with an example:
Here is the load chart:

Total load is 150 watts + 80 watts + 150 watts
= 380 watts

(2) Calculating the backup required

Now, how many hours of back up is required to run the specified load?
Say, I want 4 hours of back up i.e. when there is no sun light, battery provides the back up to run the load.Multiply the load with the backup hours and get watt-hours,
= 380 watts x 4 hours
= 1520 watt-hours
This is the amount of energy which is needed as an output from the inverter to run the load. The battery output will go to the inverter, the inverter converts dc power into ac power which in turn will run the load (fans, CFLs and fridge).

(3) Battery basics

(i) Depth of discharge:

This term tells the amount of or extent of discharge of the battery. If battery is fully or 100% charged, then depth of discharge is 0%. If the battery has delivered 40% of its energy and 60% is reserved in it, then the depth of discharge is 40%. Similarly, if only 20% charge is remaining in the battery, the depth of discharge in this case would be 80%. The batteries come with rating for DOD, here I am taking a battery with DOD 80% i.e. 20% charge is reserved. If the battery is discharge below its rated rate, it affects the performance and the life of the battery. Therefore, never discharge the battery beyond its rated depth of discharge; it shortens the life of the battery.

(ii) Capacity of the battery:

It is the amount of the charge available in the battery, expressed in Ampere-hours (Ah). 1 Ah means that a current of 1 ampere is flowing for 1 hour.

(iii) Charge rate:

The charge rate is denoted as C. It is the maximum safe rate of discharge of the battery. If the battery is rated as 12v/150 ah and C/10, it means that one can draw a maximum of 150ah/10= 15 amperes of current safely. Similarly, a 12v/150 ah battery with C/20 rating will safely provide 7.5 amperes of the maximum current.

(iv) Cycle life of the battery:

It is the number of charge and discharge cycle a battery can support before its performance falls and reduces. If a battery rated 1500 cycles, it means that it can with stand 1500 complete charging and discharging cycles before its performance reduces or falls.

(4) Calculating the capacity of the battery

Now, going back to the example, the capacity of the battery will be calculated by considering the following points:

I am taking DOD as 80% that is the 20% charge remains in the battery.
Not all the chemical energy stored in the battery is converted to the electrical energy, assuming 90% efficiency of the battery.
There will be conversion losses when the dc power of the battery is converted into ac power through the inverter to run the load. We are assuming that 10% of the energy is lost in the conversion, i.e. the inverter is 90% efficient.

Look at the following energy conversion chart:

Now, the capacity of the battery which can back up the load for 4 hours is:
0.648x = 1520 watt-hours
x = 1520/0.648
= 2345.7 watt-hours
As for the residential purposes, most of batteries have 12 volts, put this value in the equation, we get,

Capacity (x) = volts x Ah

2345.7 = 12volts x Ah
Or Ah = 2345.7/12 = 195.5 Ah
I want C/10 rated battery, so that I can withdraw a maximum current of 19.55 amperes for 10 hours. Therefore, I will look for battery having specifications as:

12 volts/195.5 Ah and C/10 rating

The nearest specification in the market is 12v/200ah battery with C10 rating & look for solar tubular battery for your solar system. You can customize your battery size based on your load requirements, hours of backup, the efficiency of your battery and inverter; the basic concept and the formulas will remain the same.

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