Difference between number of Watt-hours in different battery bank configurations

quique

Im wondering if I have battery bank A:

12v battery @ 650Ah = 7,800Wh

versus battery bank B:

48v battery @ 150Ah = 7,200Wh

Besides needing two different types of inverters, what is the difference between these two banks? Whats confusing me is that Im used to thinking that power stored is Whrs. In this way, I would think that a load pulling 10W, would last anywhere from 720-780 hours with either of these two banks.

But Ahrs is different. In this case, BB-A has 4.3 times more Ah capacity than BB-B.

Im missing something important here

BB.

Re: Difference between number of Watt-hours in different battery bank configurations

Energy is:

Watts * Hours = Volts * Amps * Hours

12 V * 650 Amp*Hours = 7,800 WH
48 V * 150 Amp*Hours = 7,200 WH

Remember that 10 Watts at 12 volts vs 48 volts gives you different Amps/Amp*Hours

Watts = V*I
I=Watts/Volts

10 Watts / 12 volts = 0.833 amps
10 Watts / 48 volts = 0.208 amps

So--Yes the AH capacity is less with the second bank--But the current draw of a 10 watt load is also 1/4 as much because of the reduced voltage.

As long as you are working in a "same bus voltage" environment (12 VDC boat, etc.), then talking about everything in Amps and Amp*Hours is fine and correct.

However, when you mix your bus voltages--Such as 12 VDC battery bus and a 120 VAC bus--Then you cannot compare a 10 amp draw without taking into account the working voltage. 10 amps at 12 Volts is 120 Watts. 10 amps at 120 Volts is 1,200 Watts... They are not the "same" bus voltage and the amp draw is not "comparable" across the two bus voltages.

When you work with "Watts"--All of the voltage/current gives you one "universal" number that works across different working voltages.

-Bill

Cariboocoot

Re: Difference between number of Watt-hours in different battery bank configurations

A couple of other notes about this.

The Amp hour rate for both batteries is measured by a equal discharge rate (e.g. 20 hour rate).
For a given amount of Watts drawn the 48 Volt system will operate at lower current, effectively 'increasing' the Amp hour capacity.
The 48 Volt system provides power at 4X Voltage, 1/4 current, thus less of the power goes to heating which makes it more efficient (by about 4%).

quique

Re: Difference between number of Watt-hours in different battery bank configurations

Ok I really didn't ask that right, although I appreciate the answers. I guess Im confused because I usually use Whrs to determine my battery bank capacity when I should use Ahrs? But then if its a 12V battery bank, then 12V adjusts for the Voltage and gives me the right number of Whrs anyway.

BB.

Re: Difference between number of Watt-hours in different battery bank configurations

In the US, anyway, I guess that everything in Amp*Hours made sense decades ago because the use of AC inverters/DC power converters was virtually non-existent. So using amps everywhere pretty much always assumed that the battery bus / working voltage was the same everywhere.

With the use of modern switching power supplies--Common voltages throughout the electrical system are no longer good assumptions.

Also--For Lead Acid Batteries--They tend to be pretty much 100% efficient when looking at Amp*Hours... Take out 55 AH from a battery bank for loads, put 55 AH back in recharging.

The "losses" are based on the fact the battery bus voltage is ~12.5 volts discharging and roughly 14.5 volts charging:

12.5v/14.5v = ~0.86 = ~86% efficiency just based on battery voltage differential

Of course, when you "gas" a lead acid battery much of the energy goes to electrolysis and heat. Equalization is almost 100% losses.

-Bill

quique

Re: Difference between number of Watt-hours in different battery bank configurations

Ok here is a more clear explanation. Let's say I have 5 loads of 10W each (10W @ 120V = 0.08A), for a total load draw possible of 50Watts. Let's say I operate them for 10 hours everyday, thats a total of 500Watt-hours per day that I need to be able to store & provide.

If my battery bank is made up of 2 - 6V batteries of 350Ahrs each in series for 12V, that means I have:

350Ahrs
or
12V X 350Ah = 4,200Whrs. (Of course I really only have about 2,100Whrs because the inverter has the LVD to protect the battery bank at about 50%.

So my question is, should my calculations say:

Load Draw of 0.08A per bulb x 5 bulbs = 0.416 Amps
For 10 hours a day = 0.416A x 10 hrs = 4.16Ahrs

or should they be more like:

Load Draw of 10W x 5 bulbs = 50 Watts
For 10 hours a day = 50W x 10 hrs = 500Whrs

Oh I see, 500Whrs / 120V = 4.16Ahrs.

Hahahaha! Its sunday!