# How Long To Charge 24v System...Is My Math Right?

Solar Expert Posts: 75 ✭✭✭✭
Hi all, I'm just trying to figure out if my math is right for charging 2 batteries hooked up in series to produce 24v from a 20watt solar panel:

Given Info

Solar Panel:
20 Watts
24v
.61A

2x 12v Batteries Hooked In Series for 24v:
24v
35Ah

Calculations:

P = VxI

For the batteries:
P = 24v x 35Ah = 840Wh

Since we already know how many watts the solar panel produces, we can simply divide the watt hours of the batteries by the solar panel wattage (20W):

Time to charge = 840Wh / 20W 42 hours

So in an "ideal world" would my calculations be correct, as I know there are other small losses to consider, but using the simple math above, would you agree around 42 hours is what it would take to charge the batteries back up to about 100%?

Re: How Long To Charge 24v System...Is My Math Right?

Yes and no... The numbers and math are correct--but there are losses and amount of sun per day... For me, I would use:
• 35 AH / (0.61 amps * 0.77 derating) amps = 74.5 Hours
I used the panel Imp rating because you would be using a PWM controller--which really uses the rated current to charge the battery, not the watts at 17.5 volts (MPPT controller could use watt rating).

Second, assume 4 hours of full sun equivalent per non-winter day:
• 74.5 Hours / 4 hour of sun per day = 18.6 days
Next, you are charging at a rate of:
• 0.61 amps * 0.77 derating / 35 AH =0.0134 = 1.34% rate of charge
Which is very near a trickle charge--or just barely keeping up with the self discharge rate--so depending on battery (flooded cell has worse self discharge, and older batteries has worse self discharge)--your actual time to recharge is even much worse (may take 2-4x longer?).

Next, batteries should not spend a long time below 75% state of charge as this is the range that batteries sulphate... So spending more than one day below 75% state of charge (technically even a few hours sufphating begins) is taking life away from your battery--so you would never want to take days/weeks/months to recharge the battery back above 75% state of charge.

One of the many reasons why we use the 5% to 13% rule of thumb for charge rate and take into account controller type+deratings when planning out a system.

When new, your panels may output more power, battery will have less self discharge, etc...--But we want the system to work for you many years from now for you too.

So we (I) like to be fairly conservative in our design guidelines/recommendations such that the system will still meet your needs for years to come.

Sorry for the long post about a "simple" question.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 75 ✭✭✭✭
Re: How Long To Charge 24v System...Is My Math Right?

Thanks Bill for the detailed answer.

Alright, so things have changed just a little from my original post.
Now I will have 2x 12v 20W panels hooked up in series which will give me a total of 1.17A

So I'm going to follow your same approach and see if I'm correct:

Total hours needed to fully recharge:
• 35 AH / (1.17 amps * 0.77 derating) amps = 38.9 Hours [fix my equation--even I confused myself with the typos -Bill]

Second, assume 4 hours of full sun equivalent per non-winter day:
• 38.9 Hours / 4 hour of sun per day = 9.7 days

Charging Rate:
• 1.17 amps * 0.77 derating / 35 AH =0.0257= 2.8% rate of charge

So with this setup, things do improve, if my math is right. I doubt my batteries will ever drain 100%, but I just like to know in the worse case scenario, how long on average would it probably take.

So it's safe to assume that it would take maybe 10-11 days to fully recharge, as I'm sure there are some other losses somewhere right?
Re: How Long To Charge 24v System...Is My Math Right?

Yep... You have the math correct.

As batteries age, they have self discharge (AGM/Sealed tend to have lower self discharge, "industrial" forklift type batteries tend to have higher self discharge)--So things can take longer.

Also, batteries have recharging losses too... AGM are ~90-98% efficient recharging, and Flooded Cell are ~80-90% efficient. Also, depending on how you cycle/recharge the batteries affects efficiency too (deeper cycling tends to be more efficient, shallow discharging to ~85% state of charge and recharging back to >90% state of charge is less efficient).

Again, being conservative, I like to use 90% efficiency for AGM and 80% efficiency for Flooded cell. So, we should add (for flooded cell in this example):
• 35 AH / (1.17 amps * 0.77 derating * 0.80 battery efficiency) amps = 48.6 Hours
Because this battery is being recharged so slowly (small solar array in this example), it would be better if the battery is not discharged much below ~75% state of charge--The longer the battery spends below ~75% state of charge, the more the plates sulfate (and reduce battery capacity). Sulfation starts in a few hours and the battery should not spend more than 1 day below 75% state of charge to reduce the amount of sulfation.

And--you should never plan on discharging the battery below 20% state of charge--Below that point, it is possible to take a "weak cell" too zero volts and actually begin "reverse charging" of the cell... That will usually kill the cell/battery outright (or within a week or two--from my experience with automotive batteries and people who have cranked-or left headlights on-their batteries to "dead").

For small battery systems (say remote monitoring site)--There are better choices for batteries (such as NiCad) which can be taken to "dead" without damage (or even be stored without charge).

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 75 ✭✭✭✭
Re: How Long To Charge 24v System...Is My Math Right?
BB. wrote: »
For small battery systems (say remote monitoring site)--There are better choices for batteries (such as NiCad) which can be taken to "dead" without damage (or even be stored without charge).

-Bill

It's funny as I was just going to ask about this, as I keep seeing and hearing over and over, you should not let your batteries fully drain or try your best to keep them above 75%, yet, I thought the point/advantage of deep cycle batteries were they allowed you to fully drain them without damaging the battery.

So then I figured, maybe cell phones, my MacBook Pro laptop, digital camera with internal battery, etc. for example use a different type of deep cycle battery, as I know I as well as many others allow their battery to come close to being dead, espically if you are out and about.

So I'm guessing mobile/portable devices use NiCad or something similar? If so, are NiCad batteries expensive, and are some solar owners using them instead of the regular deep cycle batteries (AGM/flooded etc.)?
• Solar Expert Posts: 10,300 ✭✭✭✭
Re: How Long To Charge 24v System...Is My Math Right?

cell phones and such are probably using lithium ion batteries.

nicd batteries can take more abuse, but i would not take them down below 1v per cell as they do wacky things when drained lower and they can reverse polarity too when in series.
• Solar Expert Posts: 1,973 ✭✭✭
Re: How Long To Charge 24v System...Is My Math Right?
It's funny as I was just going to ask about this, as I keep seeing and hearing over and over, you should not let your batteries fully drain or try your best to keep them above 75%, yet, I thought the point/advantage of deep cycle batteries were they allowed you to fully drain them without damaging the battery.

So then I figured, maybe cell phones, my MacBook Pro laptop, digital camera with internal battery, etc. for example use a different type of deep cycle battery, as I know I as well as many others allow their battery to come close to being dead, espically if you are out and about.

So I'm guessing mobile/portable devices use NiCad or something similar? If so, are NiCad batteries expensive, and are some solar owners using them instead of the regular deep cycle batteries (AGM/flooded etc.)?

You can take deep cycle batteries to a lower SOC than automotive batteries, but 20% is as deep as you want to go. If you can get to the tech specs for a battery, you can usually find a chart that will plot number of discharges against depth of discharge. What it will tell you is that the deeper you discharge the battery, the fewer charge-discharge cycles the battery can handle. It's a tradeoff - you can save money up front by buying a smaller battery bank and using a lot of its capacity, but you'll pay for it down the line in reduced battery life. If your system is a grid backup that won't be used very often, you can plan for a deep discharge, but if it's an off grid system that will be cycled every day, then you'll want to have a lot of headroom in your battery capacity.

Small electronics use lithium ion or maybe NiCd batteries, but their power requirements are very small compared to what you will need for a PV system. Per amp hour, lead acid batteries are cheaper than any other type by a very large margin.
• Solar Expert Posts: 75 ✭✭✭✭
Re: How Long To Charge 24v System...Is My Math Right?
niel wrote: »
cell phones and such are probably using lithium ion batteries.

nicd batteries can take more abuse, but i would not take them down below 1v per cell as they do wacky things when drained lower and they can reverse polarity too when in series.

Hmmm, do they make 12v lithium ion batteries that you can use for solar projects? I'd think they would, and if so, why aren't people using those more than using these deep cycle batteries that have all these limitations (don't discharge more than 75%..etc) you have to be concerned with. :roll:
• Solar Expert Posts: 1,973 ✭✭✭
Re: How Long To Charge 24v System...Is My Math Right?
Hmmm, do they make 12v lithium ion batteries that you can use for solar projects? I'd think they would, and if so, why aren't people using those more than using these deep cycle batteries that have all these limitations (don't discharge more than 75%..etc) you have to be concerned with. :roll:
Yes, they do, but they are hideously expensive.
• Solar Expert Posts: 75 ✭✭✭✭
Re: How Long To Charge 24v System...Is My Math Right?
ggunn wrote: »
Yes, they do, but they are hideously expensive.

That's what I figured.