Battery Bank Sizing Run Time

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Solar Expert Posts: 63 ✭✭✭
How do you calculate run time for a battery bank and inverter combination?
Using 1 each OutBack FX2524T and 4 each (1 string) Trojan T105 225 amp/hr Batteries hooked up for 24 volts, fully charged. What would the runtime be at 120vac, 2000 watt load if batteries are fully charged. Assume normal safe low battery voltage cutoff. What is formula Rule of Thumb? I will make an assumption that the run time will double with each like string added. 8)
19.76kw Solar/GT Enphase IQ7+ MicroInverters
5.40kw Solar/GT ABB/Aurora 300 MicroInverters (AC coupled to Schneider/Xantrex XW6048 output)
6.00kw Solar/Hybrid Xantrex XW6048 Inverter w/2 strings Trojan L-16E-AC Batteries (48VDC)
18kw Kohler Propane Generator

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Re: Battery Bank Sizing Run Time

Roughly, the current draw would be:
• 2000 watts * 1/23.5 volts ave batt voltage * 1/0.85 eff = 100 amps
• 225 AH / 100 Amp = 2.25 hour rate till dead
Enter in the 100 AH 250 AH and 20 Hour 225 AH rating and get Peukert Factor = 1.07

Then load the next spread sheet, enter in the capacity @ XX hour rating and find out that at that heavy discharge rate the battery will be exhausted in around 1.92 hours until dead.

Normal operation, we would discharge to 50%. Extraordinary operation (where long cycle life is not a requirement (weekend cabin/RV/UPS) you could discharge it down to 20% state of charge (80% capacity usage).

From my standard rule of thumb... I would limit current to ~40% maximum (C/2.5 surge) or ~12.5% maximum (C/8 continuous) based on the 20 Hour capacity... That would give:
• 225 AH * 0.40 * 23.5 volts * 0.85 eff = 1,795 Watts Max Surge
• 225 AH * 0.125 * 23.5 volts * 0.85 eff = 562 Watts Max Continuous
Adding parallel strings will give you slightly longer than simply the extra number of strings--Because each battery is being discharged at a slightly lower rate, so its "apparent" capacity is a bit higher at these lower rates.

Note that while I have accuracy to four decimal places--the actual accuracy is probably closer to two (just showing more numbers so you can reproduce the math--or find my errors ).

Make sense?

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 63 ✭✭✭
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Re: Battery Bank Sizing Run Time

So is this a straight forward formula to calculate Inverter run times?

Example:

Battery String Voltage = 24 vdc
Battery String 20 Hr amp rating = 225 amp/hr
Battery % of charge to be used up = 50% = .50 (if you want to use up 60% of the maximum charge then put .6 here which would leave 40% of full charge)
Efficiency and Fudge factor = .83
Another assumption is made here, that the batteries are fully charged and the name plate 20 hr amperage rating is correct. (Not to be confused with CCA)

Inverter Run time Hrs = Batt string 20 hr amp rating * Batt percent charge to use up / Inverter load in watts * Batt string Voltage * Eff & Fudge Factor
1.12 Hrs = 225 amp hr * .5 / 2000 watts * 24 volts * .83
19.76kw Solar/GT Enphase IQ7+ MicroInverters
5.40kw Solar/GT ABB/Aurora 300 MicroInverters (AC coupled to Schneider/Xantrex XW6048 output)
6.00kw Solar/Hybrid Xantrex XW6048 Inverter w/2 strings Trojan L-16E-AC Batteries (48VDC)
18kw Kohler Propane Generator

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Re: Battery Bank Sizing Run Time

Batteries have different "apparent storage capacities"--depending on current flow...

The second link shows how to calculate the battery Peukert Factor (exponent) if you cannot get it from the battery company (just need two AH capacity values for two different points (i.e., 225 AH @ 20 hour and 250 AH @ 100 hour) or load an Excel spread sheet and it will do the math.

Once you know the P.F... Then it is a "simple" calculation to figure out how long the battery will supply power at a fixed current (or use the second spread sheet).

Now--you end up with another issue--If you are using an inverter, it is not a constant current device but a constant power device:
• Power = Voltage * Current
So, the operating range of a (for example) 12 volt battery runs from ~15 volts (under charge) to ~10.5 volts (dead)... (or ~30 volts to 21 volts for a 24 volt bank).

So, as the voltage drops, the inverter draws progressively more current to keep up with the constant 120 VAC power...

I have seen a few batteries designed for UPS operation where they list battery capacity in Constant Watt Load instead of Constant Current.

I guess, it is possible to do an estimate based on constant power--your you can pick the low voltage / high current point as worst case--and do the capacity estimate there:
• 2,000 watts * 1/30 volts * 1/0.85 eff = 78 amps
• 2,000 watts * 1/24 volts * 1/0.85 eff = 98 amps
• 2,000 watts * 1/23 volts * 1/0.85 eff = 102 amps
• 2,000 watts * 1/21 volts * 1/0.85 eff = 112 amps
If your intent is not to use more than 50% capacity--perhaps yu can use 1/23 volts as your current estimate point...

Using the spread sheet, we see that ~112 amps would give the 225 AH @ 20 Hr capacity an apparent capacity of 191 Amp*Hours (C@1.7 hour rate).

Interestingly, I used the numbers for the T-105RE in the SmartGuage spread sheet and came up with P.F.=1.07 but the T-105 number from NAWS's battery FAQ is P.F.=1.25 ... If I run the above 112 amps at 225 AH and P.F.=1.25, I get: 123.5 Amp*Hours (C@1.12 hour rate).

So, obviously, there is a disconnect somewhere (T-105 is not the same as T-105RE, or there is an issue in the P.F. calculation spread sheet, or the rating numbers from Trojan are not right, or something else... I don't know). But, again from the NAWS battery FAQ--PF~1.3 for flooded cells and PF~1.10 for AGM's would indicate that the PF=1.25 for the Trojan T-105 is more than likely the correct set of numbers.

In any case--depending on what numbers you use, you can run from 1.1 hours to 1.7 hours a 2kW load on set of T-105 batteries... A fairly large spread...

But--you are probably going to hit another problem... A typical flooded cell battery can manage around C/2.5 or C*40% as a maximum surge capacity... In your case we are estimating around 102 amp load:
• 102 amp / 225 AH (at 20 hour rate) = 0.45 discharge rate
You are pretty much at the point, probably, where the chemistry is unable to keep up with the loading--so you may have the battery voltage collapse as you are exceeding its current capacity (let alone overheating the battery because of the I^2 * R self heating losses from battery resistance).

And the Peukert Factor is not a "pure" mathematically derived equation... It is really a curve fit to an observed set of data:
Peukert's effect is partially a result of slow electrolyte dispersal/diffusion and partially a result of an internal resistance that varies as a function of the discharge rate. This is what makes it so difficult to calculate. If the effect was due purely and simply to one of these effects then it would be much simpler to compute the final results.
Down load the Excel file (it is not password protected--so you can unprotect the cells and study the math) from the Smart Gauge website:
We have written you a simple Peukert calculator in Microsoft Excel format and put it on this website. This will enable you to play to your heart's desire. This calculator uses the exact same equation shown above but rearranged to a more elegant format. You can download it by right clicking here and selecting "save target as" or use the link on the left hand side.

This calculator will allow you to enter the battery capacity, the capacity rating (i.e. 20 hour rating, 100 hour rating etc) and Peukert's exponent for the battery type. It will then calculate a range of discharge currents from very low up to a discharge equivalent to the battery capacity. It then displays what is termed the "peukert corrected amps" (which is the equivalent discharge rate such a load will remove from that particular battery) for each discharge current and the available run time, again for each discharge current (note that the time is shown in hours as a decimal not in hours and minutes). Finally it shows the total amp hours available from the battery at each discharge rate.
So the answer is there is an equation that you can use to estimate the battery's apparent capacity at a set current flow (knowing the Peukert Factor), you can estimate an average current for the Inverter, and you have an estimate of the inverter's efficiency (which varies with load, temperature, battery voltage, etc.)...

And then you have other rules of thumb, which if exceeded, will bring other effects into play (Batteries not at 77F--Hot battery more capacity, cold battery less capacity; too high of current can overheat battery; too high of current can collapse battery voltage because of resistance and lack of electrolyte diffusion at high currents; etc.).

If--you are looking for a battery to supply high currents (as a ratio of battery AH capacity--Basically more than C/8 discharge continuous discharge current or more than C/2.5 surge current)--you should look at AGM type batteries--they are much better suited to that operating regime.

Am I making any sense to you at all? I am not quite sure if I am explaining the multiple issues clearly.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 63 ✭✭✭
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Re: Battery Bank Sizing Run Time

I am looking at the T-105RE not the T-105. The ones they sell here at WindSun.

I have a TrippLite UPS rated around 1700 watts sitting under my desk. I took it apart and all they have in there is 2 each 12vdc 7Ah batteries and it powers my PC, 2 each 19" Monitors, IOMega backup HDD external hard drive, Linksys wireless access point, phone charger, etc for nearly an hour. I know the load is no where near 1700 watts load but it is a very very small battery compared to a 4 each Trojan T-105RE's so 4 each 225 Ah Trojan's have to last longer. Right?

Now I am maybe looking at going with the Xantrex XW6048 and using 8 each Trojans or other batterys to get to 48vdc for longer run times and split the loads between both sides of the 240vac circuits to get 2 each 120vac circuits. That would make it around 1000 watts/leg.
19.76kw Solar/GT Enphase IQ7+ MicroInverters
5.40kw Solar/GT ABB/Aurora 300 MicroInverters (AC coupled to Schneider/Xantrex XW6048 output)
6.00kw Solar/Hybrid Xantrex XW6048 Inverter w/2 strings Trojan L-16E-AC Batteries (48VDC)
18kw Kohler Propane Generator

• Solar Expert Posts: 1,989 ✭✭✭
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Re: Battery Bank Sizing Run Time

If your doing this for a UPS type application, don't use flooded battery's, go with AGMS.
• Solar Expert Posts: 63 ✭✭✭
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Re: Battery Bank Sizing Run Time

What are the advantages and disadvantages to using the different battery types with the inverter?
Why would AGMS be selected for this application?
19.76kw Solar/GT Enphase IQ7+ MicroInverters
5.40kw Solar/GT ABB/Aurora 300 MicroInverters (AC coupled to Schneider/Xantrex XW6048 output)
6.00kw Solar/Hybrid Xantrex XW6048 Inverter w/2 strings Trojan L-16E-AC Batteries (48VDC)
18kw Kohler Propane Generator

• Solar Expert Posts: 1,989 ✭✭✭
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Re: Battery Bank Sizing Run Time

http://www.windsun.com/Batteries/Battery_FAQ.htm
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Re: Battery Bank Sizing Run Time

Are you using the Tripplite UPS as a UPS, or will this be attached to solar powered battery bank for significant off-grid use?

AGM's are very good for UPS applications that use a lot of power for 15-30 minutes (very low internal battery resistance and ability to deliver a large amount of current for short periods of time with small capacity batteries). And you don't have to check the water level every month while the system is on standby.

If this is for an "off grid" setup--check the efficiency of the UPS--They may (or may not) be as efficient as some of the inverters designed for solar systems.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 63 ✭✭✭
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Re: Battery Bank Sizing Run Time

This is going to be on a grid connected system with a biomass steam driven generator supplying power and co-gen on a distribution system not a transmission system. This inverter system will be to supply power to the PC's, and various connected control equipment when the grid fails for about 30 minutes or so until the diesel generator can be started and come online to supply local power not export. What currently happens is whatever took the utility offline also takes the steam driven generator offline. We sometimes feed 4000 kw back to the grid and the local town is connected to the same distribution system and consumes 4000-4500 kw so if the utility drops the local town then we might not even feel it or know that it happened until the utility comes back online with us no longer in sync since the utility does not have a sync check relay in their system. We must protect ourselves so when we sense this happening we open our utility tie breaker and leave it open until our sync system re-sync's back to the utility and recloses our tie breaker.
19.76kw Solar/GT Enphase IQ7+ MicroInverters
5.40kw Solar/GT ABB/Aurora 300 MicroInverters (AC coupled to Schneider/Xantrex XW6048 output)
6.00kw Solar/Hybrid Xantrex XW6048 Inverter w/2 strings Trojan L-16E-AC Batteries (48VDC)
18kw Kohler Propane Generator