How to calculate UPS battery backup

When I first asked this question myself, a friend of mine kindly sent me to the manual (a joke, obviously). In the meantime, I found out that calculating ups batter back up is not such a big deal as I might have thought in the first place. In order to make everything as clear as I can, I will use a small example. Let us assume the following ideas:

Inverter efficiency of UPS battery is 90% (the norm is somewhere between 90% and 98%)
Battery end point voltage 1.67 (usually specified on the UPS itself, or in its manual)
Environmental temperature 77F

Assuming that we know the following things about our UPS : one string of batteries, 30 each, UPS rating 40kW and 6 cells per unit, we can break down the calculations in three steps:

1.) Actual battery load for 40kW

40kW … 90% efficiency means an actual 44.4kW load (you can calculate this by dividing the rating of the UPS by inverter efficiency – 40/0.9 = 44.4kW)

2.) Watts per Battery

44.4kw (previously calculated) will be divided by the number of batteries we have available, and the result will lead to 1481 watts per battery. (you can calculate this using the equation: 44.4Kw/30 = 1481W)

3.) Watts per each Cell

Giving the necessary data we will deduct that each cell needs 247W. (calculate this using the equation: 1481W / 6 (the number of cells per unit) = 247 watts per each cell)

Now we can easily estimate the run-time of your UPS battery back up system. Giving the fact that we know that each batter has about 247W per each cell, and we have a battery end point voltage of 1.67V your run time should be somewhere between 45 minutes and 60 minutes.

Various Other Formulas to calculate backup time
  • Battery current at full load / Battery Ah. This gives approximate backup time.
  • Battery AH/Battery current at full load. Ex:160/40 amp we get three hours back up
  • Battery Ah*dc cut off voltage of ups/load(VA)
  • Battery Ah*nominal dc voltage of system/load in VA
  • Battery capacity X No of battery X Ah X battery(0.8)/ o/p wattage. This is will give backup time for your setup
Related articles