# Uninterruptible Power Supply work from battery duration

I am going to buy an UPS, and on website that sells is written that model contains battery with capacity 9 Ampere-hours, 12V DC output voltage and UPS resulting output voltage is 220 AC.

On the page it is written, that with 100 Watt consumer connected, UPS, working from battery will last for about 24 minutes. I do not understand why.

Power equation is

$$P = V • I$$

So, if power is 100 Watt and voltage is 220, then current is 100/220 = 0.4A. Hence, if capacity is 9Ah, it should last for 9/0.4 = 22 hours.

Even if by voltage, the battery voltage should be taken, and we have 100W/12V = 8.3A, then, still it should work more then 1 hour.

What am I missing? Additional power loss on voltage transforming from 12 to 220?

• Battery voltage is lower than output voltage. Calculate the Wh in the battery and the output Wh needed instead. Assume less than 100 % conversion efficiency. Dec 2, 2022 at 10:58
• Two likely areas: Inverter inefficiency and battery derating. The inverter is never going to be 100% efficient, so you will lose power there, and a significant number of battery chemistries don't like being fully discharged/floated at full charge. Potentially only 50% of the batteries stated capacity is available for use. Dec 2, 2022 at 11:00
• You haven't mentioned the UPS, but if this is a SLA battery with 50% derating, the thats 4.5 Ah available, 100W/12V = 8.3A draw, so 22 minutes for 8.3A to exhaust 4.5Ah sounds about right. Dec 2, 2022 at 11:03

A battery may be stated as having a capacity of 9 Ah but many circuits won't be able to use all that capacity and, in your particular case that is self-evident. If the load is 100 watts and, it can be powered or sustained for 24 minutes then you need to refer that back to the 12 volt supply.

You do this by estimating the DC to AC conversion efficiency. This is usually no better than 80% hence, for a 100 watt AC load, your battery may be subject to a 125 watt DC load. The current will be 125 watts ÷ 12 volts which equals 10.42 amps.

If the battery and the circuit working together can only sustain load this for 24 minutes, that's a usable battery Ah rating of 4.2 Ah.

If the DC to AC power conversion efficiency is only 70% then your 12 volt battery may be seeing a DC load equivalent to 143 watts. That's a current of nearly 12 amps hence, for 24 minutes, that's a usable Ah rating of 4.76 Ah. Take your pick.

It's a little more complex than this if you dig into the details of course.

• Maybe, You have some experience, how much capacitance do I need make monitor and some basic phone charger work for 2 hours from battery then? Dec 2, 2022 at 11:34
• How much load power @Stdugnd4ikbd Dec 2, 2022 at 11:43
• @Stdugnd4ikbd As a rough rule of thumb (80% efficientcy and 50% derating), you need 2.5x the capacity. So (power needed/ battery voltage) * 2.5 * time needed should give you the Ah rating needed. Dec 2, 2022 at 12:04
• @Andyaka I think monitor is 30 W, charger same Dec 2, 2022 at 20:05
• Well you can probably assume more than 60 minutes but, it really does depend on how power efficient your inverter is and, there's nothing I can help you with there unfortunately. Dec 2, 2022 at 21:03

You've invented a perpetuum mobile! Or maybe not...

Yes, you have to go by power. 0.4A from the 12V battery would be 4.8W. You can't magically make 100W from that.

So P on both sides of the conversion has to be the same (and than losses have to be accounted for) So this simple Forumula applies. $$U_1 * I_1 = P = U_2 * I_2$$

So you did the right thing looking at the Power. Now the capacity of a battery is somewhat special. If you have a high current the usable energy from the battery is reduced. And you can't ( and should not ) use a battery to zero. So assume that at 100W you can only use 50% of the stated capacity of the battery. And than subtract some non ideal working conditions (batteries neither like heat nor cold) and less than ideal conversion (80% efficiency is considered quite ok for an inverter; technically they could get well above 90% but it's getting expensive than) and suddently you're close to what the datasheet states.

The battery Ah rating is a value when battery is fully discharged during 20 hours. So an 9 Ah 12V battery has 9 Ah if discharged with 0.45 A for 20 hours, or rather, discharged at C/20.

If you want to power a 100W load, the battery current is more than 8 amps, so more energy goes into losses inside the battery, so it cannot provide 9 Ah for 1 hour if discharged at about C/1.

Add losses from conversion in inverter.