# formula for battery amp hours / watts used etc

Posts: 35Solar Expert
Can someone post a formula for the following or help me with the math.

Im looking at 2 105t trogans (12v total in series).. so 225ah.

my estimated loads are as follows:

(all the below will only be in use fri-sun at most)
108watt hrs? 12v water pump 9amps - 1hr use day
312watt hrs? 6 x 13watt cfl - 4 hrs day
200watt hrs? 25watt fan x 8hrs day
100watt hrs? 50watt tv/sat 2 hrs day

720watt hrs day approx.

So would the 2 t105s be able to handle that without to much drain?

I went from 1- 135watt panel & 4 t105s
to
2- t105s and 2 -135watt panels (better match maybe)

I have a genny and will have a 30 amp iota charger when the solar doesnt keep up (weekend only cabin)

Thanks!!!

Chris

p.s. live in S. IL

• Posts: 17,615Banned ✭✭
Re: formula for battery amp hours / watts used etc

Chris;

Getting the numbers absolutely precise is tricky. But you can get darn close. Good enough for government work.

Watt hours are Watts * hours. Using a Kill-A-Watt meter can get much more accurate results than multiplying the rated Watts by the estimated hours of use. That's the load side. For now let's assume 720 Watt hours daily is right.

What can you get out of a pair of T105's?
The most you want to discharge them would be 50%, so you have 112.5 Amp hours to work with.
In actuality, the rate of depletion is not linear - but it's hard to calculate that way so you can use the nominal Voltage as an approximate mean. That's 112.5 * 12 = 1350 Watt hours. Since that's nearly double the expected use, it would probably work.

Now that you're in the ball park you have to start examining things more closely. For instance, including the power draw of the inverter. That could be 20 Watts over 24 hours: another 480 Watt hours. All of a sudden you're a lot closer to that maximum potential.

Looking at the panel capacity it is woefully insufficient. Using the famous "Icarus Formula" for an approximate AC yield we get:
270 Watts * 4 hours / 2 = 540 Watt hours

It looks like you'd need one more 135 Watt panel and an inverter that doesn't suck up too much power to be good to go.

But check the loads first. The more accurate you can be on that the happier the outcome.
Re: formula for battery amp hours / watts used etc

Regarding the Battery bank:
• 720 watts * 1/0.85 system efficiency * 1/12 volt battery = 71 AH per day
• 225 AH * 1/0.50 maximum discharge = 112.5 AH (for long battery life)
• 112.5 AH usable capacity / 71 AH per day = 1.6 days of battery use
Not bad at all... You should be fine.

Regarding rate of charge:
• 2x 135 Watts of panels * 0.77 charge derating / (225 AH * 12 volts) 0.077 = 7.7% rate of charge
Rate of charge is in the middle of our 5% to 13% rule of thumb--So, again, this should be OK...

Using PV Watts for St Louis MO:
```Month    Solar Radiation
(kWh/m 2/day)
1      3.60
2      4.22
3      5.09
4      5.40
5      5.67
6      5.83
7      5.86
8      5.50
9      5.33
10      4.83
11      3.53
12      3.02
Year      4.83
```
Your average power usage of 720 watts will require:
• 720 Watts * 1/0.52 system derating / (2x 135 watt panels) = 5.1 Hours of Sun minimum
So, you are just above breaking even during the summer... So, you are probably OK for a weekend cabin.

It would not hurt to get one more panel to reduce genset use--but if your power estimate is correct and you only have a few weeks a year when people are there for more than a few days at a time--the genset will be fine for a bit of extra power (couple hours of run time in the early morning every few days type thing).

You might want to look into a Battery Monitor--especially if spouse, kids, guests will be using the cabin when you are not there... It is much easier to tell them to start the genset when they see 50% on the meter (and turn off when >80%) than to have them measure specific gravity with a hydrometer.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Posts: 134Solar Expert ✭✭
Re: formula for battery amp hours / watts used etc

Bill- the calculations that you posted seem nice and clear...

Can I assume that I could use the same calculations for any system?
For example... If my estimated cabin daily load is 600 watts... In Adirondack Park NY and I plugged in my 600 watts into this calculation, I get the following...

Battery Bank:
600 watts * 1/0.85 system efficiency * 1/12 volt battery = 59 AH per day
225 AH * 1/0.50 maximum discharge = 112.5 AH (for long battery life)
112.5 AH usable capacity / 59 AH per day = 1.9 days of battery use

Rate of charge:
2x 135 Watts of panels * 0.77 charge derating / (225 AH * 12 volts) 0.077 = 7.7% rate of charge

Using PV Watts for Albany NY:

1 3.20
2 4.12
3 4.29
4 4.95
5 5.48
6 5.30
7 5.67
8 5.45
9 4.93
10 4.00
11 2.42
12 2.33
Year 4.35

600 Watts * 1/0.52 system derating / (2x 135 watt panels) = 4.27 Hours of Sun minimum

So if I understand correctly... I can also use a similar system of 2-130 Panels and 2 t105 batteries... correct??

Since the 4.27 Hours of Sun requirement is very close to the 4.35 year average, I shouls also consider a third 135 watt panel?

I do have a question regarding the batteries... Since spanel originally stated that hes 2 batteries would be in series, wouldn't this make it a 24 volt system? Therefore the calculations should use 24v instead of 12v????
• Posts: 17,615Banned ✭✭
Re: formula for battery amp hours / watts used etc

The Trojan T105 is a 6 Volt battery. Two in series is 12 Volts.

You're always happier when you round the results in the right direction. In this case, going for the minimum calculated number of panels will be disappointing. My usual recommendation is to shoot for 10% charge rate and you'll probably get somewhere between 5% and 10%. Remember that loads running while charging reduce the net charge rate. That's why I use this basic formula for off-grid:

Amp hours * 0.10 = target peak charge Amps * charge Voltage (Trojan: 14.8 ) = Watts needed. Less efficiency derating (77% typically) = array size.

So for one set of T105's you get:
225 * 0.10 = 22.5 Amps * 14.8 = 333 Watts / 0.77 = 432 Watt array ideally.
Four 135 Watt panels @ 540 Watts would be best, but three @ 405 Watts falls in between 5% and 10% and will work under most circumstances. Remember that this calculation relies on good sun, and Albany in Winter is shy on that (look at the PV Watts data) so having 540 Watts would probably work better in December.

The other thing to look at is the Amp hour "consumption & harvest", but usually if you get the charge rate Amps target in line and don't heavily discharge the bank (more than 33%) you're okay with that. Otherwise you look at it like this: 540 Watts @ 77% = 415 / 12 Volts nominal = 34 Amp hours * "hours of equivalent good sun" (usually 4) = 136 Amp hours harvest. That's 60% of the batteries' capacity, so it should cover most days. If 3 hours of sun is all you're likely to get it's still 45%.

And you can use the quick "Icarus Formula" for figuring AC Watt hours from Panel size:
540 Watt array * 4 hours equivalent good sun = 2160 Watt hours / 2 (50% over-all efficiency) = 1080 Watt hours on the AC side.

Nobody every complained of having too much panel (except for paying for them), but most of the complaints we get around here are a result of having too little.
Re: formula for battery amp hours / watts used etc

Coach,

Yes--you have it right, but besides the 6 volt battery issue that Marc mentioned... You should never plan on running a solar PV system at "rated power" or expecting to use 100% power every day (if 600 watts per day is a very consistent number). You should plan on supporting your base load assuming using 50% to 75% per day (allow for stretches of cloudy weather guests over, occasional heavier use of power).

So--if these were a cabin used all year--typically I suggest people plan on 9+ months of generator free use, and 3 months when you will use the genset to make up for poor water--So in the above example tossing out the bottom three months, gives us October at 4.0 hours of sun per day as our "break even month".

Also, the formula I gave is a bit awkward for calculations... And easier one to use (plug into a spread sheet) would be:
• 600 watt*hours per day * 1/0.52 system eff * 1/4.0 hours of sun per day = 289 watts of panel minimum
Another rule of thumb is we suggest 1-3 days of battery storage and 50% maximum depth of discharge (longer battery life)... So--picking 2 days of no-sun, 600 watt*hours of AC power usage per day with an 85% efficient inverter on a 12 volt battery bank:
• 600 WH * 1/0.85 invrtr eff * 2 days of no sun * 1/0.50 max discharge * 1/12 volt battery bank = 235 Amp*Hour @ 12 volt bank
2x 6 volt * 225 AH "golf cart" batteries would be close enough (if you wan to round down).

But, we also suggest a rule of thumb for the rate of charge for a battery bank of 5% to 13%. So, we need to check that out too. Using 10% rate of charge (20 Hour Rate from Mfg. Spec)--we would get a suggested solar array size of:
• 225 AH * 14.8 volt charging * 1/0.77 panel+charger eff * 0.10 Rate of Charge = 432 WH minimum of solar array
So, in this case, the minimum array size would be based on our battery bank size and rate of charge choice of 432 watts (vs the 289 Watt based on 9 months of sun calculation with 600 watt load).

You can roll back to 289 watts minimum and still be over the 5% rate of charge suggested for a 225 AH 12 volt Trojan battery bank (1/2 of 432 W = 216 watt array).

Anyway--Lots of formulas you can plug in for your own needs... Using a kill-a-watt hour type meter to measure your daily power needs (example of a k-a-w meter showing 0.600 kWH per day or 600 Watt*Hours per day) will help you dial in your load requirements.

For an off grid system--if you can stay at or below ~3.3 kWH per day or ~100 kWH per month (full time using electricity with heavy conservation for a "near on grid" life style--no A/C)--Is a pretty cost effective and reasonably priced Solar PV system.

Also, when you look at using AC inverters--You may need to take into account their "standby" loads... An inverter running 24x7 hours a day (for example to run an Energy Star frost free refrigerator) may take 20 watts with no load--So:
• 20 watts * 24 hours per day = 480 WH per day extra "losses"
So, the whole process of defining the battery bank and supporting solar array is iterative as you define your eventual requirements and the specific supporting equipment.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Posts: 134Solar Expert ✭✭
Re: formula for battery amp hours / watts used etc

Thanks guys.. this is very clear.

Regarding the batteries. Instead of using two 6 volt 225 ah golf cart batteries, would I be better off using two 12 volt 110 ah AGM batteries in series?
That would give me a 24 volt system and allow for smaller cable sizes. Using the AGM batteries would allow me to store them indoors and no maintenence.

Yes- using 540 watts of panels appears to be the smart way to go since my winter sun is limited.

I know that AGM batteries and an extra panel will end up costing more but,,, if it saves me headaches in the long run, I don't mind.
• Posts: 17,615Banned ✭✭
Re: formula for battery amp hours / watts used etc
Thanks guys.. this is very clear.

Regarding the batteries. Instead of using two 6 volt 225 ah golf cart batteries, would I be better off using two 12 volt 110 ah AGM batteries in series?
That would give me a 24 volt system and allow for smaller cable sizes. Using the AGM batteries would allow me to store them indoors and no maintenence.

Yes- using 540 watts of panels appears to be the smart way to go since my winter sun is limited.

I know that AGM batteries and an extra panel will end up costing more but,,, if it saves me headaches in the long run, I don't mind.

You could up the system Voltage and halve the Amp hours and current rate for the same amount of over-all power, yes.

One caution about AGM's: they are unforgiving of overcharging (too high Voltage) and you can't check the SG on any sealed battery. A good accessory for AGM's is a battery monitor to keep track of the SOC (which you can't otherwise do). That will cost more money - and needs proper programming to be accurate which can be tricky.
• Posts: 1Registered Users
Re: sound good here is a better idea

I read that some are saying to get another 130 watt solar panel ! if you do it would only make sense to also get another 112 or 120 amp hour battery- that way the solar panels can recharge all the batteries during the week while your not there, and you will have even more power with one more 112 amp hour battery - remember to also get a solar charger regulator so the solar panels dont over charge the panels while you not staying in you cabin- you can buy a good solar charger with lcd dispaly on line , i saw some for around 30 \$ and it was a 30 amp capacity so you can probably hook it up to you entire battery bank- and let it be fully charge during the week ! also getting even 2 more batteries would only make sense because then you wont have to worry about the power drain and they will all be recharged up during the week- its always better to have more solar power and battery power then you need - so I suggest maybe 1 more solar panel and two more batteries- i just was at wall mart and saw some deep cycle marine 122 Amp Hour batteries for areon \$89 dollars that is here in the mid west though i guess Walmart prices may vary state to state town to town - but walmart is i think the cheapest place to buy deep cycle marine battery witch is what i use for my solar power system !and for around 90\$ dollars you cant beat the price- if you need to match the battery packs with the others you have just get 2 and add your new panel to the new batteries !