How to calculate sufficient battery backup power?

[NuLED]

Hi guys,

Please help me understand how to make this calculation.

I have a 23 Watt inductive load, a fish tank pump that I need to keep running to circulate water and keep things aerated and filtered in my aquarium.

I want to make a battery backup for it, so that it works even when the power goes out.

I want to place it under a solar panel (or at least have it switchable to solar at a moment's notice) and get it powered through a 12V car battery.

I have an inverter that provides up to 60 watts (designed for 12V battery).

I want to know A) what is the mAh (or whatever) battery capacity I need and B) what is the minimum wattage I need to keep that battery charged via solar.

I read before that car batteries have something called Cold Crank Amps which I assume is the peak amperage it can provide at an instant (not constant load) so I reckon that should be OK to start up the pump, which is inductive.

I am running off 110/120V (I guess).

 

[(*steve*)]

As per another question, this page gives some information.

If you can determine the power factor of the motor, you can use this to determine the apparent power of the load (VA).

Unfortunately, you need to size your UPS (VA) to be able to supply the full apparent power.

There are other threads where I've discussed how to size a solar array, and believe me, you need comparatively huge arrays because you need to ensure the system still runs during cloudy periods in winter when there are shorter days.

 

[Y2KEDDIE]

Battery Capacity

The battery required may make this not feasible. Your ampacity required will be what your inverter draws under full load (pump, pumping). You will most likely find is your inverter is very inefficient, it draws more current idling that the motor itself. A better alternative would be to use a DC motor on the pump and operate it directly from a DC charger/ battery combination.
To calculate the current or ampere/ hour battery you need: measure the current drawn by the inverter while connected to the running motor. Multiply the current measured times the number of hours you want it run when AC power is not available. This is the Amp/hrs needed.
A little bit more is needed for charging, and this is determined on how fast you want to recharge. If you lose Ac power and your battery runs down, you most likely will want to charge it fast to get things running. That’s going to require lots of solar cells!
Batteries are rated in Amp/hrs, but seldom does one need full amperage for only one hour. Amp/hrs give a big number and looks good for marketing, but typically a 12 A/hr battery is more like 1A for 10 hours and it drops off fast the last few hours. This varies with different batteries. You really need more A/hrs for reserve.
Most people don’t realize how big a battery system is required to operate loads over a period of time. It’s not cheap. Consider your car battery: it uses a lot of amperes for engine starting in short bursts, then it provides less, but considerable current to run the accessories while the engine is running. The 3 phase alternator/ rectifiers are supplying 30 -40 Amps to recharge, taking horsepower from the engine.