How To Calculate Ah (Amp hours) and Wh (Watt hours) of a Battery Bank
I will use my own off-grid battery bank for this example how to calculate its total Amp hours and Watt hours.
I’m not going to get into the little details and caveats. But this will provide a quick overview to figure it out. Maybe it will provide some insight for your own alternative energy battery bank one day.
Okay, lets go…
My objective was to put together a 48 volt battery bank (this is DC volts we’re talking about) with enough Watt hours (kWh – kilowatt hours) of energy storage to at least operate my essential systems for a few days before requiring recharge. I utilize an approximate 4000 watt solar panel array to recharge by way of a charge controller followed by a DC > AC inverter system.
Why 48 volts? Because it’s more efficient (than say, 12 volts), less loss, less current, and most off-grid inverters like to chew on 48 volts…
So, there are all sorts of battery types and voltage configurations. I’m not going to get into all that. Instead, I’m going to use 12-volt batteries in this example because that’s what I used on this particular battery bank.
My batteries are 12 volts each and rated for 100 Ah each (amp hours). What about the Amp hour rating? Put simply, you might say that this battery (if drained down to ‘dead’) will provide 1 amp for 100 hours. Or 20 amps for 5 hours. Depends how you look at it… You get the picture?
(Well, technically a fully charged 12-volt battery while at rest, no load, would be 12.7 volts. But I’m not getting into that sort of detail with this general principle.)
[ Read: Battery State of Charge ]
Volts times Amps equals Watts. So this one battery will provide 12 x 100 = 1200 Watt hours. Or 1.2 kWh (kilowatt hours) of energy.
To get to 48 volts, I strung (connected) four batteries in series. So that string provides 48 x 100 = 4800 or 4.8 kWh of energy.
I put together 6 strings of 4 batteries in series. Then I wired all six of those strings in parallel with each other. So that made 6 x 4800 = 28800 or 28.8 kWh of stored energy.
I sketched out a simple block diagram to illustrate my battery bank:
These are lead acid type batteries. Although more specifically they are AGM (Absorbent (or Absorbed) Glass Mat (or Material)) so I can keep them indoors without off-gassing.
All batteries have a cycle life versus depth-of-discharge curve. The deeper you regularly discharge them, the sooner they’ll die off. These parameters vary quite a bit depending on the specific battery type / chemistry which I won’t get into here. But I just wanted you to know that.
Given my specific battery type, I avoid discharging them further than 30% off the top (30% DOD or depth of discharge). This greatly helps with overall cycle life of the battery bank in my case.
So that means I will try not to use more than 30% of 28.8 kWh, or, about 9 kWh of energy for my given battery bank before recharging.
That’s enough to provide me with a few days of “juice” for my essentials, such as my furnace during winter (also tied with my hot water), refrigerator, chest freezers, and well pump.
We have lots of cloudy winter days here, so it works out pretty good. During summer I have “tons” of energy, so I run my whole house (including air conditioners) on the system. Although the AC’s go off at night (power hogs).
Okay, that was just a quickie on figuring out battery bank Amp Hours and Watt Hours.
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When it is time for battery replacement, have you checked out the LiFePO4 battery technology ?
I have seen impressive demonstrations on them. Smaller foot print for the same energy or greater energy density. More expensive than LA batteries.
No financial interest in any of this…
I have written about that battery technology a few times. Many advantages. Costs a bit more, but you get “return” on that investment in a number of ways.
Iron Edison RE-Volt Lithium Iron Phosphate Battery
8 Advantages of Lithium-ion Batteries for Off-Grid Energy
I switched from lead acid to LiFEPO4 and love them. No more adding distilled water. I also never had a good idea what state of charge the lead acid batteries were. They say you can use a hygrometer to test lead acid state of charge but I tried several and they were very imprecise. I would test the same battery multiple times and get different results.
Great information. Thank you!
Very timely as I was able to test out my Lights Out kit I built for the CPAP machine. I was fortunate enough to be without grid power for 5 days during our Texas ice age. I planned on writing a contributing article once we are fully recovered from the storm damage. Amazingly a 100 amp AGM ran 8 hours before I recharged from the generator pushing a CPAP that draws 3.7 amps per hour.
More to follow and I’ll needs Ken’s math skills to properly build an affordable set up for anyone on a fixed income.
Have you considered minimizing battery imbalances by matrixing your battery? The idea is that your six strings are cross tied (preferably with fused links) to prevent battery hide out. Take your diagram with the major home run current paths, then inter-connect the positives (and separately your negatives) with smaller wire gauge fused runs, straight down on your diagram to create a balanced matrix that will equalize charge currents.
Yes, I have implemented measures to balance it. I just didn’t want to get into the little details in the post above. However in short, my interconnecting cables for each parallel string are cut to the same length (the longest required length set the dimension for the rest) and tied/bonded at a single point (for both positive and negative). This achieved a perfectly balanced situation. Additionally, each string is fused.
If you are concerned with battery life, you will also need to keep them in the A/C as well. High heat will eat away at their life span… although they do store more power that way. Batteries like to be kept at 68 degrees and only cycled to 30% DOD.
If you’re daring enough, consider using an alternate electrolyte such as phosphoric acid which has no sulfur, so cannot sulfate your plates! You’ll loose 30% capacity off the top, but will gain much more life span. Cell voltage will also be slightly lower at 1.9v vs the normal 2.1v, but adding on extra cells would bump it back up. Also do not discharge below 1.7v per cell or crystals will form.
I’m in the process of building a very similar battery bank as the one you have, 48v with 24 12v a batteries at roughly 75ah. For best efficiency should the inverter be picked to run at close to max capacity or should I aim at running at 50-75% of its capacity. I am looking at 5kw and 8kw. In my mind the 5kw is plenty for most of our everyday load uses but I feel it would be nice to have the option to go higher.
To Altaprep, Here’s my opinion… I would not design a system such that the inverter is running at maximum. Whenever my inverter runs near full throttle, it definitely gets hot – and I can even smell it…. In fact, I’ve accidently overloaded it a number of times recently (running too many window air conditioners along with everything else), and it tripped out automatically. Whoops… So, if I could do it all over again, I would have bought a bigger capacity inverter. Maybe one day I’ll upgrade. If you’re considering a 5K versus 8K, I would go with the 8K to have a margin. That’s my opinion.
That’s a great point, I will be definatly leaning towards the 8k
My goal is to run the battery bank as a back up for outages What would you suggest for solar panels output as a maintenance to keep the batteries fully charged?
Thanks a lot for the info!