Question

A household’s daily energy usage is 800 Wh. The operating voltage is set at 24 V. Day of autonomy required is 4 days and the manufacturer only allows the battery to have a minimum state of charge of 50%. Calculate the minimum sized battery bank in Ah that would meet the household’s load requirements?

Answer 1

Concept:

Ques : What does the size of the battery bank mean?

Ans : This means that we need to find out how much charge should be stored inside the battery to meet the household load requirements. The charge stored is indicated by the capacity of the battery , measured in

amp-hours (Ah). It depends on the energy stored in the battery and the operating voltage in the following relationship-

Where

: Energy stored in the battery, measured in watt-hours (Wh).

: Capacity of the battery, measured in amp-hours (Ah).

             : Operating voltage, measured in volts.

Solution:

In the question, the daily energy use of the house is 800 Wh. When the household runs on battery for 4 days or 4 x 24 hours, it consumes-

This amount of energy should be stored within the battery to power the household for 4 days.

From the first equation,

But this is not the answer !!

Commercial batteries generally have a minimum state of charge between 30-50 per cent. This means that the battery will discharge up to 30-50 % of its capacity and this limit is set to prevent permanent damage to the battery. The minimum state of charge in the question is set at 50%. We therefore need the size of the battery, of which 50 percent is 3200 Ah.

Hence, the battery capacity must be at least 6400 Ah to meet the household’s load requirements.

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Thank you :)