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 bhcva 10-06-2012 03:39 PM

Battery capacity - Peukert stuff

I'm finally getting to understand the significance of the Peukert equation. I'm assuming that if one ties two six volts into one 12v bank it would not change the results of the equation (amp-hours remains the same). If one adds another pair (or more) doubling the rated amp-hours available, it seems logical that one would use the new amp-hour figure as input to the equation. Doubling a 242 ah bank to 484 ah and using the 484ah in the equation more than doubles the number of minutes available at a given current draw by something on the order of 10%. Just curious...am I off base here?

 Stu Jackson 10-06-2012 11:37 PM

Re: Battery capacity - Peukert stuff

I don't think so. The P equation has only time and discharge amperage involved, Cp= I n t where n is a log function of I and t. It has nothing to do with battery bank capacity, it tells you the difference in time remaining when larger draws are made.

In fact, most battery monitors, if they're like the Links, only affect the time remaining function and NOT the amp hours consumed. Why? 'Cuz the only effect the Peukert function has is time remaining (which, of course, HAS to be based on any given battery bank capacity). That's simply linear -- bigger bank, bigger time remaining.

The Link manuals, especially the Link 2000, are pretty good at explaining this stuff. Xantrex has a discontinued models manual download section on their website.

The P equation essentially says: a higher load beyond the 20 hour rating takes more out of a bank, of ANY size, a lighter load takes less.

If you do the math on the exponential function, you'll see the differences.

In the real world, if you are imposing unusually larger loads on your house bank, it'll last less time because higher draws reduce the power availability, but only on time remaining, not on amp hours consumed.

That said, it really makes little difference.

Do the math. :)

 bhcva 10-07-2012 09:40 AM

Re: Battery capacity - Peukert stuff

"That's simply linear -- bigger bank, bigger time remaining."

True, but that's the question...is it really linear if multiples of batteries are coupled. The P equation has five inputs as you know - the only one that could change if I enlarge the bank is the available amp hours. If I double up batteries to double the amp hours available I could just double the minutes available as computed from the single battery configuration; or, I could use the now doubled available amp hours in the P equation and I will see that the available minutes at any amperage more than doubles by something on the order of 10%. Which way is correct?

 Stu Jackson 10-07-2012 10:50 AM

Re: Battery capacity - Peukert stuff

Cp = I (current) * exp n (from a logarithmic function of times over currents) * t (time)

That's all it does and says. The "inputs" to calculate "n" are logs of time1 and time2, over logs of I (current) 1 & 2.

Time 1, time 2, current 1, current 2 are the four variables used to calculate n. That's four.

Anyway, the answer to your question is that a bigger bank, twice the size, would have twice the time to go based on similar loads. That's all.

The part you seem to be confusing is the P (Peukert's factor) with the doubling of your bank capacity.

The P doesn't change, it stays the same based on the type of battery you have.

Does that clear it up? Based on your first post, are we using the same equation?

 asdf38 10-07-2012 01:36 PM

Re: Battery capacity - Peukert stuff

Quote:
 Originally Posted by Stu Jackson (Post 930366) I don't think so. The P equation has only time and discharge amperage involved, Cp= I n t where n is a log function of I and t. It has nothing to do with battery bank capacity, it tells you the difference in time remaining when larger draws are made. In fact, most battery monitors, if they're like the Links, only affect the time remaining function and NOT the amp hours consumed. Why? 'Cuz the only effect the Peukert function has is time remaining (which, of course, HAS to be based on any given battery bank capacity). That's simply linear -- bigger bank, bigger time remaining. The Link manuals, especially the Link 2000, are pretty good at explaining this stuff. Xantrex has a discontinued models manual download section on their website. The P equation essentially says: a higher load beyond the 20 hour rating takes more out of a bank, of ANY size, a lighter load takes less. If you do the math on the exponential function, you'll see the differences. In the real world, if you are imposing unusually larger loads on your house bank, it'll last less time because higher draws reduce the power availability, but only on time remaining, not on amp hours consumed. That said, it really makes little difference. Do the math. :)
Stu I don't think that's quite right. When you add another battery in paralel you're adding more capacity but you're also cutting down the load on each battery. This makes it non-linear.

A 100Ah (@20 hour rate) battery can supply 5 amps for 20 hours.

Two of these cells in paralel are rated for 20 hours at 10A. Running them at the 5A from above means they're now operating at half their reference rate and they'll go for more than 40 hours because of the equation. So for a given load, doubling the capacity more than doubles the real-life time.

I ran through the math and it bears this out (note the capacity is within the exponential). It's about 10% as bhcva said.

 Stu Jackson 10-07-2012 02:10 PM

Re: Battery capacity - Peukert stuff

That's true. All I'm saying is that doubling battery capacity has NOTHING to do with the Peukert's Factor for any given battery. Of course, when you add battery capacity, the batteries will last longer because the % draw (assuming the SAME load) will be less on a larger bank. What the P Factor does is correlate the time remaining for batteries based on larger loads than the standard 20 hour rate.

Like this:

IS IT BETTER TO HAVE ONE OR TWO BATTERY BANKS FOR HOUSE USE?
(By Nigel Calder - I DIDN’T write this!!!)

The popular arrangement of having two house banks alternated in use needs scrutiny before I go any further.

LIFE CYCLES: As we have seen, the life expectancy of a battery in cycling service is directly related to the depth to which it is discharged at each cycle - the greater the depth of discharge, the shorter the battery’s life.

This relationship between depth of discharge and battery life is NOT linear. As the depth of discharge increases, a battery’s life expectancy is disproportionately shortened. A given battery may cycle through 10% of its capacity 2,000 times, 50% of its capacity 300 times and 100% of its capacity around 100 times.

Let’s say, for arguments sake, that a boat has two 200-ah battery banks, alternated from day to day, with a daily load of 80 Ah. Each bank will be discharged by 40% (80 Ah of one of the two 200 Ah banks) of its capacity before being recharged. The batteries will fail after 380 cycles, which is 760 days (since each is used every other day). If the two banks had been wired in parallel, to make a single 400 Ah battery bank, this bank would have been discharged by 20% of capacity every day, with a life expectancy of 800 days, a 5% increase in life expectancy using exactly the same batteries!

But now let’s double the capacity of the batteries, so that the boat has either two 400 Ah banks, or a single 800 Ah bank, but with the same 80 Ah daily load. The two separate banks will be cycling through 20% of capacity every other day, resulting in a total life expectancy of 1,600 days. Doubling the size of the battery banks in relation to the load has produced a 210% increase in life expectancy. The single 800 Ah bank will be cycling through 10% of capacity every day, resulting in a life expectancy of 2,000 days - a 25% increase in life expectancy over the two (400 Ah) banks, and a 250% increase in life expectancy over the single 400 Ah battery bank!

There are two immediate conclusions to be drawn from these figures:

1. For a given total battery capacity, wiring the (house) batteries into a single high capacity bank, rather than having them divided into two alternating banks, will result in a longer overall life expectancy for the batteries.

2. All other things being equal, any increase in the overall capacity of a battery bank will produce a disproportionate increase in its life expectancy (through reducing the depth of discharge at each cycle).

FOR BATTERY LONGEVITY, A SINGLE LARGE (HOUSE) BANK, THE LARGER THE BETTER, IS PREFERABLE TO DIVIDED (HOUSE) BANKS.

 Maine Sail 10-07-2012 02:41 PM

Re: Battery capacity - Peukert stuff

The Peukert number for a given battery does not change when the individual batteries are placed in parallel. For example a 100Ah 12V battery with a Peukert of 1.25 will still have a bank Peukert of 1.25 when you have four in parallel for 400Ah's. So the Ah capacity of the 4 100Ah batteries in parallel is 400Ah's with a Peukert of 1.25.

One one hundred Ah battery will support a 5A load for 20 hours before hitting 10.5V

Four 100Ah batteries wired in parallel will support a 20a load for 20 hours before hitting 10.5V. Go above the 100Ah load of 5A, with a single 100Ah battery, and you have less capacity. Go above the 20A load on a 400Ah bank and you also have less capacity. Conversely use less than 5A or 20A and you'll get more than 100Ah's or 400Ah's....

 asdf38 10-07-2012 02:50 PM

Re: Battery capacity - Peukert stuff

Stu, that's all right but previously you said this:
"Anyway, the answer to your question is that a bigger bank, twice the size, would have twice the time to go based on similar loads. That's all."

That's either contradicting the reasoning in the passage you just quoted, or it's confusing.

Again to the OP's question, he's right, doubling the capacity with either an additional cell or a larger cell results in a 10% "bonus" capacity because of this equation.

 Maine Sail 10-07-2012 03:08 PM

Re: Battery capacity - Peukert stuff

Quote:
 Originally Posted by asdf38 (Post 930515) Stu, that's all right but previously you said this: "Anyway, the answer to your question is that a bigger bank, twice the size, would have twice the time to go based on similar loads. That's all." That's either contradicting the reasoning in the passage you just quoted, or it's confusing. Again to the OP's question, he's right, doubling the capacity with either an additional cell or a larger cell results in a 10% "bonus" capacity because of this equation.
If we look at capacity, and the average load, on a bank with a Peukert of 1.25, we can look at it like this:

The boat uses an average of a 5A load.

100Ah bank at a 5A load will deliver 100 Ah's. (50 Ah's usable to 50% SOC)

200Ah bank at a 5A load will deliver 238 Ah's (138 Ah's usable to 50% SOC)

300Ah bank at a 5A load will deliver 395 Ah's (245 Ah's usable to 50% SOC)

400 Ah bank at a 5A load will deliver 566 Ah's (366 Ah's usable to 50% SOC)

 Stu Jackson 10-07-2012 09:13 PM

Re: Battery capacity - Peukert stuff

I've done an analysis of this on a spreadsheet. This shows that the percentage useable and delivered increases proportionally but that as the bank gets larger the increase in differences from the next smallest bank decreases.

I've tried to re size the original spreadsheet into gif and bmp files with no success. It'd sure be nice to be able to post a link with the XLS file, but this board doesn't include that feature.

Short of that, I'll go scan a printout of the spreadsheet and post it as a jpg.

Limiting at best. Bummer.

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