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Calculating Ampere-Hour AH requirement

We are in a sorry state of erratic and long power cuts, due to shortage of power production by the nation against the increasing load conditions.  To add fuel to this fire, a wholesome of abled people putting their hard earned money on to power backup solutions, where they store the power during power availability and consume the stored power during outage.  On the whole, this looks simple and elegant, but this is not doing any good to the state, which shed’s power at different locations to balance against shortage in power production.  So theoretically, in a place where a family consumed 1kW per hour, would consume 2.5kW per hour during power availability and generate 1kW during power outage.  Yes, you are right. The equation is not balanced, because atleast 30-50% of power is wasted during the backup-retrieve cycle.

Ok, coming to the point.  What is the solution? Go for harvesting solar power, availability in abundance and omni present.  And most interestingly, rationed to perfection based on the amount of un-shadowed free space a family has.  I will just limit this article to calculating the battery provisioning when you go for a solar-inverter solution.  Let’s say I want to have a power backup for 2 hours and my load is 1kW. What would be the ideal inverter solution for this load condition?

Normal Power 1000 Watts
Power Factor 80 %
Inverter Rating 1000W/80% = 1250 VA
Number of Backup Hours 2 Hours
Energy To be Stored 1000×2=2000Wh
Inverter Battery Voltage 24VDC
Battery Amp-Hours 2000/24=83AH
Add @30% AH Margin 83*1.3=108AH~100AH

So, for this configuration you need a 1250VA Inverter with 2x12v 100Ah battery bank.  Let me explain the calculation,

  1. Power Factor: In AC (alternating current), Power = Voltage x Current x Power factor unlike in DC, Wattage = Voltage x Current.  Power factor is measure as the cosine of the phase angle between voltage waveform and current waveform.  For home use, the power factor will be 0>PF<1.  When PF is lower, the efficiency of the system suffers a lot.
  2. Battery Voltage: For 1250VA inverter system, the choice of battery bank is 24V instead of 12V.  The rationale for this choice is to limit the current from the battery to the inverter unit.  If you use a 12V battery bank, at full load there will be a current of 1250/12=104A flowing from the battery to the inverter.  You may have noticed the thickness of the battery wire be very high.  Despite that the power loss on those wires when the current is 100A, would be much higher than it is with 50A on a 24V system.  For a 24V system, the peak current shall be 1250/24=52A.  Also, at 100A, with 1m cable between battery and inverter, the impedance should be 0.00001 ohms.
  3. AH Margin: Although battery AH rating considers absolutely draining of the battery, we will not be able to do that for normal SMF battery.  Meaning, we should not discharge below 10V and likewise should not charge beyond 13.6V per 12V battery.  In order for the AH rating to work, we have to apply atleast 20-30% margin.

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