# Battery Capacity calculations

Posts: 48Solar Expert
Could you guys please check over my calculations for determining battery bank sizing.

Watts * Efficiency of array&charger * (1/charge voltage) * (1/rate of charge) = Battery Amp Hours

Which i believe is correct. The part i'm questioning is the charge voltages:

for 12v i'm using 14.5v as the charge voltage
for 24v i'm using 29.0V as the charge voltage
for 48v i'm using 58V as the charge voltage

Are these correct values?

If you want to give it a test or have any suggested fixes/improvements let me know. Battery Bank Calculator

Any corrections or suggestions is appreciated!

• Posts: 10,311Solar Expert ✭✭✭✭
Re: Battery Capacity calculations

doesn't look right to me.

take a known pv like a us 64 that i have. now 77% of that is 49.28w. to translate this to current one needs to divide that by the vmp of the pv and the us 64 is 16.5v. others are usually higher than this so one size voltage does not fit all. anyway, 49.28w/16.5v=2.9867a. to figure the battery capacity now depends on the % charge rate employed.
5%=59.73ah
10%=29.87ah
13%=22.97ah

now that works for a pwm cc and it gets more complicated when using an mppt cc as the vmp then gets changed (usually downward) and the current output is higher and is made somewhat variable by the mppt action, but generally i'd say another 10% in current on average.
Re: Battery Capacity calculations

Looks nice. You might want to have a little "FAQ" that lists why you used 14.5 volts instead of 12.0 volts, why a AGM (low self discharge/high efficiency) battery might work better at 5% rate of charge vs a flooded cell (or worse yet; forklift) battery that have higher self discharge, less charging efficiency, etc...

You could also put a 1% rate of charge in for Floating/Storing batteries too (boats, etc.)--We get a fair number of those questions too.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Posts: 48Solar Expert
Re: Battery Capacity calculations

Neil.. So should i add in a vmp box to make it more fine tuned or make it more general for the masses. My calculator on the page lets you select a charge rate between 5-13%

Bill - Good advice on the float charge. Ill add that in. Do you have a post or page with some info on the diff batteries vs charge rate (AGM/flooded ect) to gain some info for the faq?

I'm slowly building calculators/tools to help figure out the stuff i initially struggled with! I figure it will help solve alot of the random questions for my self and other in the community!
Re: Battery Capacity calculations

Some good places to start:

Deep Cycle Battery FAQ
www.batteryfaq.org

It does get very complicated very quickly... It it why here we try not to tell people to "search" for the answers on the forum, or cut and past a "newbie" post for everyone that asks how to buy/build an off grid system--But, instead try to answer the question in the way each new poster asks the questions (I some panels; I have some batteries; I want to run a freezer for a day; etc.).

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Posts: 48Solar Expert
Re: Battery Capacity calculations

Neil - to answer your early question about why 14.5v - Float charges generally range from 13.02 to 13.20 volts and the absorption charging stage generally ranges from 14.2 to 15.5 volts. so 14.5 seemed like a happy medium.
Re: Battery Capacity calculations

I think what Niel was also trying to point out... Power=Voltage * Amperage (yes, I know you know that ). But when spec'ing solar panels/arrays and MPPT vs PWM controllers, the Vmp vs Vbatt does make for some differences...

Say you have a 175 watt solar panels with Vmp=17.5 volts, then (using round numbers):
• Imp = Pmp / Vmp = 175 watt panel / 17.5 vmp = 10 imp amps

Now when looking at the charging characteristics of a PWM controller, as long as Vmp-array-operating-temp > Vbatt-charging, the current from the array is (roughly) Imp (at noon-time 1,000 w/m2. So, the "nominal power" charging a "12 volt battery" near 14.5 volts from a 175 watt panel would be (PWM controllers usually have very operational current requirements--so we will ignore it here):
• Pbatt-charg = Vbatt-charg * Imp = 14.5 volts * 10 amps = 145 watts (noon time sun)
• Eff = Pbatt-charg / Pmp-rated = 145 watts / 175 watts = 0.829 = 83% efficiency

Note the efficiency here is purely based on the "mismatch" between Vmp-panel and Vbatt-charging:
• 14.5 Vbatt-chrg / 17.5 Vmp = 0.829 eff

And, technically, as the panel gets hot and Vmp-panel depresses, with a PWM controller, it does not change the Imp of the panel (Imp slightly rises with temperature--but we can ignore it here).

Remember we used 0.77 derating for solar array (which, mostly, is 82% derating for Vmp-hot depression) and ~95% efficiency for a MPPT controller running somewhere near maximum rating (most efficient point).

The same thing done with a MPPT controller:
• 175 watts * 0.77 derating * 1/14.5 volts batt = 9.29 amps into battery

So--we are assuming a hot panel, some dirt, controller, wiring losses... Using the "extra" 6% derating on a PWM controller (0.83 eff PWM - 0.77 eff MPPT):
• 10a Imp * 0.94 = 9.4 amps for our "paper derating" of the PWM controller

So the "calculated" difference between 83% derating for a PWM vs 77% derating for a MPPT controller--I chose to round down the ~6% to account for aging/voltage-wiring drop/dirt/etc. with the PWM controller and call it "close enough" for solar work.

For very cold climates, the MPPT controller can add 10-15% or so to energy collection. But, the useful part of MPPT (in my humble opinion) is it allows you to use larger wattage panels that do not output 17.5 Vmp (large panels are cheaper). And it allows you to run Vmp-array to upwards of 100 VDC (depending on brand/model of MPPT controller)--Which makes it much easier and cheaper to send power longer distances (between Array and Battery Shed) using much smaller gauge wiring.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Posts: 10,311Solar Expert ✭✭✭✭
Re: Battery Capacity calculations

bill is correct and i'd say go ahead and put the vmp into the calculator with a note that mppt can see higher currents. also note that downconversions by mppt controllers can really muddle up someone from being able to figure out what the current actually is. you are getting the idea that it is hard to nail down what is going on with solar even from one moment to the next, but for the purpose of calculating battery bank capacity it may suffice as a rough minimum from a pwm standpoint.

one has to watch what conclusions one can draw with the observed currents from calculations resulting from the use of the calculator as low vmps will show higher currents based on the formula power in watts = volts x amps. it is true you could see higher currents with low vmp for a given pv stc wattage rating, but during the warming from the sun and hot ambient temps this could drop too low to place a charge into the battery. on the other extreme one may put a pv with a vmp for example of 23.9v and on a pwm controller this does not up the current available to the battery, but wastes the extra power as the excess voltage is pretty much ignored from benefiting the battery as only an mppt controller will bring any excessive voltage into usable power through downconversion.

i commend you on trying to simplify the figuring of a battery bank's capacity, but as you can see it's not so simple.
• Posts: 48Solar Expert
Re: Battery Capacity calculations

So if I add in the panel vmp voltage then i also need to add in PWM or MPPT to get a more accurate estimation... you are right! this is slowly getting more complicated! I'm still determined to figure it out (or atleast a very good educated guess of a calculator).. that being said if you guys know of any other common formulas you use let me know and Ill see if i can make some "simplified" calculators for the community.
Re: Battery Capacity calculations

I have seen some pretty sophisticated spread sheets that do a very good job of taking many issues into account (including voltage/Peukert factors/etc...). And--For Me--They really required a lot of knowledge to use correctly and interpret.

What would be neat is to have something that you can put in some information (amount of loads, XXX watt of panels, YYY AH @ ZZ volt battery bank, etc.)--Then the rest of the information that can be derived is then filled into the blank areas... For example:

Things people want:
• how many batteries do I need (5%/10%/13% rate of charge)
• how many watts of solar panels
• how much power will system produce
• how much does the system cost

• Minimum hours of sun (4 hours for 9 month system; 5 hours for 4-6 month "summer" system)
• AH @ battery volts of load per day
• WH of load per day
• I have YYY AH of ZZ volt batteries
• I have AAA Watts of panels
• I want 1/2/3 days of battery storage (default 50% maximum discharge)
• ~82% panel derating (from STC)
• ~95% efficiency for MPPT charge controller / GT Inverter
• ~85% efficiency for off grid inverter
• ~90% efficiency for AGM battery
• ~80% efficiency for Flooded Cell Battery
• ~C/8 maximum continuous load from flooded cell battery
• ~C/2.5 maximum surge load from flooded cell
• ~C*4 maximum load for AGM
• ~5% to 13% Rate of Charge for Battery Bank (flooded/AGM)
• ~C/20 = 5% rate of charge for GEL
• ~80% efficiency for AC Battery Charger (typical)
• ~0.67 PF for non-PFC (power factor corrected) AC battery charger (PF=1 for PFC charger)
• ~5% to 25% rate of charge for AC Battery Charger
• ~\$5 to \$8 per Watt (of solar panel) GT system
• ~\$10 to \$20 per Watt (of solar panel) for Off Grid system
• 0-1,200 Watt load -> 12+ volt battery bank
• 1,200 watt to 2,400 watt load -> 24+ volt battery bank
• over 2,400 watt load -> 48 volt battery bank

I can come up with equations to relate the major pieces to each other--But trying to figure out a useful interface for the above would be a bit of work too.

Do you setup different input screens for each major set of starting questions (battery, solar array, loads)? And then the output screen below has the "answers".

And where do you put the "tweaks"? For some, do you instead output a battery bank based three calculations like 5/10/13% so people can see range instead of having to put a different number and get a different result?

As you can probably see from my answers before--I tend to like to give the 100/200/260 AH battery bank answer (5/10/13%) so people can see the "range"... Obviously, there are many physical devices (like batteries/panels/inverters) that come in set sizes... I.e., 220 AH vs 280 AH battery--And not 260 AH. Sort of gives people an idea of what is a "big" vs "small" difference in relation to the overall system.

And, many times, stuff will have to be recalculated... They come up with a range of 200-260 AH battery bank, and pick 280 AH--So now they need to resize the Solar array for the 5-13% rate of charge...

Can become a very interesting human interface/design project in itself (iterative updating as people select exact values to finalize and print out for there design).

As you can see--that is why I choose, for example, to "collapse" the power differences between PWM and MPPT--And make their choice based on system size (less than 200 watts PWM, over 600 Watts probably MPPT; or MPPT because there is a long distance between Solar array and battery/charger shed) rather than worry about 5-15% better performance complexity in calculations for some folks that have sub freezing winters.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Posts: 112Solar Expert ✭✭✭✭
Re: Battery Capacity calculations

shift-

Thanks very much for your contribution to the community. Sometimes folks question the accuracy of a contribution when there are typos in the wording. In that spirit, I offer the following:

"Finding the correct solar array power to battery bank Amp hour (AH) [ration] ratio will ensure your batteries stay happy and live a long time. If you have [two] too small of an array for your battery bank, it will not have enough current to properly charge; alternatively [to] too high of a charge rate may “cook” your batteries. In general, you want to stick with a 5-13% charge rate. If you just want to float charge your batteries, pick a charge rate of 1-2%. You can calculate this using the formula Watts * Efficiency of array&charger * (1/charge voltage) * (1/rate of charge) = Amp Hours… or just use the calculator below!"

I do not know enough about off-grid PV systems to offer any technical comments, but your calculator is of interest to someone like myself who might consider off-grid requirements, and be interested in sizing a system.
• Posts: 4,536Solar Expert ✭✭✭✭
Re: Battery Capacity calculations

Shift, I like your idea, good concept..

As to developing an all-in-one formula I think it can be done if there is a default value of 1 fro any variable, if a specific value is not entered on the input page. If you are familiar with Access there would be default values entered in the 'Mask" for the variable, other wise it is overridden with the entered value... make sense?

Once you get the formula page done , just protect (lock) the entire page, so the formulas are sacrosanct... with Values grabbed from an Input page.

HTH

KID #51B  4s 140W to 24V 900Ah C&D AGM
CL29032 FW 2079/ 2073/ 2054 175A E-Panel WBjr, 3 x 4s 140W to 24V 900Ah C&D AGM
Cotek ST1500W 24V Inverter,Omnicharge 3024,
Linksys Wet54g WiFi Bridge, ASUS RTN10 router, Hughes1100 Sat Modem
Eu3000i & 1000i Gens, 1680W & E-Panel/WBjr to come, CL 647 asleep
• Posts: 6,869Solar Expert ✭✭✭✭
Re: Battery Capacity calculations
westbranch wrote: »
.... If you are familiar with Access....

NOOOOooooo Not ACCESS ! Just use a spreadsheet, not a database !!
Powerfab top of pole PV mount | Listeroid 6/1 w/st5 gen head | XW6048 inverter/chgr | Iota 48V/15A charger | Morningstar 60A MPPT | 48V, 800A NiFe Battery (in series)| 15, Evergreen 205w "12V" PV array on pole | Midnight ePanel | Grundfos 10 SO5-9 with 3 wire Franklin Electric motor (1/2hp 240V 1ph ) on a timer for 3 hr noontime run - Runs off PV ||
|| Midnight Classic 200 | 10, Evergreen 200w in a 160VOC array ||
|| VEC1093 12V Charger | Maha C401 aa/aaa Charger | SureSine | Sunsaver MPPT 15A

solar: http://tinyurl.com/LMR-Solar
gen: http://tinyurl.com/LMR-Lister ,

Re: Battery Capacity calculations

I think his intent is to run this from a web server--not any sort of down-loadable spread sheet (other than maybe the results--my suggestion).

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Posts: 4,536Solar Expert ✭✭✭✭
Re: Battery Capacity calculations

Mike,Shift, sorry, did not mean to use Access , just as an example...

KID #51B  4s 140W to 24V 900Ah C&D AGM
CL29032 FW 2079/ 2073/ 2054 175A E-Panel WBjr, 3 x 4s 140W to 24V 900Ah C&D AGM
Cotek ST1500W 24V Inverter,Omnicharge 3024,
Linksys Wet54g WiFi Bridge, ASUS RTN10 router, Hughes1100 Sat Modem
Eu3000i & 1000i Gens, 1680W & E-Panel/WBjr to come, CL 647 asleep
• Posts: 1,571Solar Expert
Re: Battery Capacity calculations

Shift, I think this is a great idea and will be very useful for people new to off-grid solar.
One issue though, is that if you're going to all the trouble of doing a calculation like this, then I wouldn't use the panels-to-battery charging ratio as the basis of the calculation because this is very rough- more of a finger in the air, rather than a real design tool. The main problem I have with that formula is that it doesn't let the user choose the amount of autonomy they want from the bank (i.e. how many days of no-sun should it handle), nor does it let the user select the depth of discharge of the bank. Since you can use a computer to do the calculations you could go for a more detailed formula and let the user supply more variables- and then you could supply default "middle of the road" values for some of the more technical variables.

The formula I like to use and an example XLS to do the calculation can be found here: http://www.casanogaldelasbrujas.com/blog/2008/01/04/sizing-an-off-grid-photovoltaic-system-2/

• Posts: 10,311Solar Expert ✭✭✭✭
Re: Battery Capacity calculations

many have to watch the days of autonomy thing as this expansion of a battery bank affects the rate of charge. this can stop a proper charge from occurring. you cannot arbitrarily expand on capacity and expect it to still charge the same as if it were charging in a single day's rate with the smaller battery you originally sized the charging for in that single day. if your daily design for instance requires a battery bank of xx ah and you charge it at a good 10% rate that expanding that capacity to 5x that for 5 days of autonomy will reduce that charge rate to 2% and will not properly charge the battery. people who think they can expand capacity without expanding the charge are fooling themselves even if you only need the small current due to small loads. in this 5x case you would need to minimally raise the charge rate to about a 5% rate whether you need it for loads or not.
• Posts: 1,571Solar Expert
Re: Battery Capacity calculations
niel wrote: »
people who think they can expand capacity without expanding the charge are fooling themselves even if you only need the small current due to small loads. in this 5x case you would need to minimally raise the charge rate to about a 5% rate whether you need it for loads or not.

I think we've been here before, and I don't agree I think you need to increase the PV size a bit, but not directly proportionally to the battery size. Just looking at my own system (sized at a 5% rate), even now in the beginning of spring the system only ever pulls 100% from the panels for the first 3 hours of the morning. By 10am it hits absorb and starts reducing the power, so a smaller array would have been just fine. Sure, for those extremely rare events when I actually do draw the battery bank down to 50% (it still hasn't happened yet), a smaller array would take longer to charge the bank- but as long as those events are rare- it won't hurt the battery that much.

Don't you think that for someone living in the dry south of the US who doesn't want to use a generator and has the money to spend- that they can size a battery bank for 5 days of autonomy without adverse effects?

Stumbled on this note from Trojan the other day: http://www.trojanbattery.com/BatteryMaintenance/ChargerSelection.aspx the bit says:
When selecting a charger, the charge rate should be between 10% and 13% of the battery's 20-hour AH capacity.
...
Chargers with lower ratings can be used but the charging time will be increased.
• Posts: 10,311Solar Expert ✭✭✭✭
Re: Battery Capacity calculations

stephen,
if you look i did not say it needs to parallel the pvs to the capacity. if that were the case the pvs would've increased by that same 5x increase the batteries would've seen. my point was you still need around that 5% minimum to give a proper charge to the batteries as my example had shown. the new charge rate would've been that 2% rate which is too small to charge the battery. the actual loads don't become the dictating factor when you are out that far in autonomy. i don't care how it's twisted to appear good, you will need that 5% minimum so autonomize all you like as long as you can give at least around that 5% charge rate. you have that 5% minimum and even you know 2% would not work.
Re: Battery Capacity calculations

I usually run both set of numbers... 5-13% rate of charge and 1-3 days of autonomy based on energy usage and hours of sun.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Posts: 2,680Solar Expert ✭✭✭✭
Re: Battery Capacity calculations

Well, opinions do differ on the exact max charge rate available from PV. My system calculates to be about 4% of capacity from PV. Do have generators and chargers here, that can do about 13% charge rate without any PV input. To me, if one's system reaches Float almost every day, the occasional need for 10-ish% rate can be provided by gensets and AC chargers. Some battery manufacturers recommend occasional high-rate charge (C/10), to renew plate exposure to the electrolyte, thus maintaining capacity.

This approach works for my system with my batteries. Batteries do need more charge as they age, as they become somewhat less eficient. Will add some more PV to systems here, but this is not due to need, just doing the addition because it is fun, and can reverse even more of my previous conservation measures.

Different battery technologies can have somewhat different needs. And, always consult the battery manufacturer's data for information on any specific battery. YMMV, Vic
Off Grid - Two systems -- 4 SW+ 5548 Inverters, Surrette 4KS25 1280 AH X2@48V, 11.1 KW STC PV, 4X MidNite Classic 150 w/ WBjrs, Beta KID on S-530s, MX-60s, MN Bkrs/Boxes.  25 KVA Polyphase Kubota diesel,  Honda Eu6500isa,  Eu3000is-es, Eu2000,  Eu1000 gensets.  Thanks Wind-Sun for this great Forum.
• Posts: 48Solar Expert
Re: Battery Capacity calculations

Lee - thanks for the spell check!

I have the week off work so I'll see if i can get more tweaks built into the calculator this week

I also got my 400w of solar panels mounted.. so ill do a little post with pics once i finish "prettying" up the wiring