# Time it takes to fully charge a battery from 40% discharge state

3 Posts
Apr 5, 2010 06:16 am
Time it takes to fully charge a battery from 40% discharge state

I’m planning to hook up some rechargeable batteries to power an inverter where solar power will act as the only rechargeable source for the batteries. I have the battery amp hour for my battery bank as 999AH at 200Volts on a 40% DoD. So I wanted to calculate what kind of solar panel will be able to fully charge the battery from its 40% DoD to full power at 5 sun hours.

After a bit of research, I found somewhere on the internet that to know how long it takes to charge a battery with a given supply of current (amps) the commonly used formula is

Charge time = 1.2 x Amp hours (of the battery being charged) / charge current

From my own understanding, this formula is to charge the battery from it fully discharged state to it’s full power. If so, I assume, the formula to charge the battery from a 40% discharge state would be:

Charge time = 0.4 (1.2 x Amp hours (of the battery being charged) / charge current)

Is this formula correct?

Furthermore, I assume the charge time that will be gotten from using this formula represents that of a battery that is idle. Will the formula (ie charge time) be the same as when the battery is being charged while it's in use? If not, can you please give me the formula for charge time when the battery is in use? As the solar power never powers the inverter directly but all its power is always used to recharge the batteries.

Thanks in advance for the help.

« Last Edit: Apr 5, 2010 07:14 am by Sorbari Akpea »

220 Posts
Apr 6, 2010 03:57 am
Re: Time it takes to fully charge a battery from 40% discharge state

Hi Sorbari Akpea,

i think we see a good book title here!: (hey brother can you spare two hundred grand) subtitled: (how to have fun with fifteen thousand pounds of lead)

"Charge time = 0.4 (1.2 x Amp hours (of the battery being charged) / charge current)

Is this formula correct?"

that equation looks good..that one gives us a very optimistic 80% efficiency for the chemical conversion. seems that is the standard starting point...i find that battery based systems tend to run closer to the 50-60% mark at the end (in a good design!) after all the system losses

everyone comes to find their own methods for working through some of these calculations and perhaps others may have some tips on other methods...but for me i just seem to get into trouble when i attempt to work with units of amp hours (tend to make silly apple/oranges mistakes) i find it much easier to convert all units into watt hours as a first step.

how some of the numbers look from here:

999AH @ 200volts = 199,800 watt hours

40% discharge (60% remaining) = 79,920 watt hours used

79,920 X 1.2 = 95,904 to recharge back to full

95,904 needed/5 hours = 19,181 watt pv array (need to do the 80% thing again with that too!) = 23 kw array

the good news is that if we use some power during the day while charging we get to skip that 80% chemical conversion thing and use it as it's being made..sort of..but those watt hours not going into the battery still need to be made up for with a longer charge time.

i hope this is a "paper" project and not an actual system.

have fun! dave

3 Posts
Apr 7, 2010 12:13 am
Re: Time it takes to fully charge a battery from 40% discharge state

It is a "paper" project at the moment. My friend and I are relatively new to renewable energy and we are really excited about it. So at the moment we are swapping ideas to see if we can build one, a “useful“ one. But yeah, I understand what you mean about the book title...

Anyway, I wanted to ask another question.

Can a 12 volt 1400 AH battery plugged into a 1500 watt inverter take 5.4 hrs to fully charge from its 40% discharge state when it is not in used (switched off)?

To get the charge time, I used the formula you used above.
12 V x 1400 AH = 16,800 watt hour
At 40% discharge state = 6,720 watt hours used
6,720 x 1.2 = 8,064 to recharge to full state
8,064 needed / hours = 1500 watts
Hours = 8,064 / 1500
= 5.4 hours

Is this correct?

P.S. I don’t understand why you multiplied the watt used by 1.2. What is the 1.2? And what is the answer gotten? Amp hour?

Furthermore, I don’t understand what you meant earlier about 80% chemical conversion. How do I reduce my result now from it's 80% to 50%.

Thanks in advance for any help

« Last Edit: Apr 7, 2010 07:55 am by Sorbari Akpea »

220 Posts
Apr 8, 2010 05:40 pm
Re: Time it takes to fully charge a battery from 40% discharge state

Sorbari Akpea,

looks like you may be understanding this better than you think you are.

you will enjoy these links on the workings of battery chemistries and their charge/discharge characteristics.

http://www.smartgauge.co.uk/technical1.html

http://batteryuniversity.com/

that multiplication factor of 1.2 is an effort to recoup the 20% losses..example: if we take away 100 units, we need to replace it with 120 units to get back to where we started.

you will notice in those links (and explained A LOT better than i ever could) how our battery stores it's energy as a chemical reaction.

afraid we have to get back into the subject of amp hours here as well. drill into that smartgage site where they talk about ah ratings and how the charge/discharge rates effect it's efficiency...many of the batteries used in RE setups carry a rating of C20 (5% of it's capacity) example: a 100ah battery discharged at 5% (or 5 amps) will last 20 hours.(those are full cycle ratings to 100% dod) we stay well above that.. ie: your example of 40%, some folks only go to 20%.

in your above 1400ah example we see that our charge rate is up around the C10 rate (~10% of capacity) and may effect the charge efficiency..some batteries (ie:gell) have problems with higher charge rates and others (ie:agm's) seem to be able to take all you can give them.

to complicate matters more, there are charge acceptance ratios to consider..again explained better in the links. but in a nutshell. we can put the "bulk" of the charge back into the battery with speed and ease but the last 10% or so will only go back in so fast..<- this last bit is a pita in these RE systems and seems to force us (me at least) to run our systems with the battery running in 70-90% state of charge range and only charging up to 100% during our maintenance schedule.

YIKES! looks like i'm rambling on here.

one more link, the AltE store has an interactive calculator for battery/grid systems that gives a good feel for sizing a battery bank and pv array.

http://www.altestore.com/howto/Tools-Calculators-Reference/c36/

cheers, dave

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