Calculation of parallel string battery currents
- Thread starter Solarod
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Variation in what quantity are you asking about?
I see the numbers of the out of balance configurations to be maybe 3+ amps out of 30 or roughly 10%.
If it is wired right should it be within 2%? Say a 200 amp load and the four are all 48 to 52 amps do we say that is fine. Or should they be within 1 amp or start looking for an issue. Or 100 mA?
This is the whole theory vs practice thing.
I have two in parallel and a heavy draw might 68 and 75 amps. Inverter comes off one end of a short bus with four terminals and each battery is connected to one of the middle studs. Wire is very close to same length. I think I want to review mine again.
If it is wired right should it be within 2%? Say a 200 amp load and the four are all 48 to 52 amps do we say that is fine. Or should they be within 1 amp or start looking for an issue. Or 100 mA?
This is the whole theory vs practice thing.
I have two in parallel and a heavy draw might 68 and 75 amps. Inverter comes off one end of a short bus with four terminals and each battery is connected to one of the middle studs. Wire is very close to same length. I think I want to review mine again.
Are you referring to one of the calculated Examples? If so, cite which one. In post #3 I gave 3 examples of the calculated out of balance for 3 different values of battery IR. Could you be more specific please. I could do a special calculation if you can give the battery IR and link resistance.
Perhaps you're asking about sensitivity to a failure of all the battery IR's to track. Let me run an example. Set the battery IR's to 1 milliohm, typical for a somewhat high IR of modern LFP batteries, set the link resistance to 1 milliohm, higher than what a good busbar setup would give you. Then using the 4 battery parallel hookup with a diagonal connection, I calculate these currents in amps:
Example 16
37.5
12.5
12.5
37.5
Now if the link resistance is set to 1/10 milliohm (this is busbar range), the currents become
Example 17
27.3
22.7
22.7
27.3
But let's see what happens with my change to the connection load as given by the yellow and blue in post #26. The battery IR is still 1 milliohm except set the IR of battery 3 to 1.1 milliohms--a 10% increase, and link resistance set back to 1 milliohm. The currents are now:
Example 18
25.1
25.4
24.0
25.5
This is still very good. To get balance not even this good with the red and black connection in post #26, we had to decrease the link resistance from 1 milliohm to 1/10 milliohm. So a 10% increase in one batteries' IR caused a fairly small increase of imbalance. Compare to the imbalance of the standard diagonal connection even when the battery IR of all the batteries matched. To get better balance, but not even as good as Example 17 we had to decrease the link resistance to 1/10 milliohm; this is the range you could get with thick busbars. The yellow/blue connection was better than this even with a 10% mismatch in the IR of one of the batteries, and with link resistance much higher than you'd get with thick busbars.
Example 16
37.5
12.5
12.5
37.5
Now if the link resistance is set to 1/10 milliohm (this is busbar range), the currents become
Example 17
27.3
22.7
22.7
27.3
But let's see what happens with my change to the connection load as given by the yellow and blue in post #26. The battery IR is still 1 milliohm except set the IR of battery 3 to 1.1 milliohms--a 10% increase, and link resistance set back to 1 milliohm. The currents are now:
Example 18
25.1
25.4
24.0
25.5
This is still very good. To get balance not even this good with the red and black connection in post #26, we had to decrease the link resistance from 1 milliohm to 1/10 milliohm. So a 10% increase in one batteries' IR caused a fairly small increase of imbalance. Compare to the imbalance of the standard diagonal connection even when the battery IR of all the batteries matched. To get better balance, but not even as good as Example 17 we had to decrease the link resistance to 1/10 milliohm; this is the range you could get with thick busbars. The yellow/blue connection was better than this even with a 10% mismatch in the IR of one of the batteries, and with link resistance much higher than you'd get with thick busbars.
Yes #16 something needs fixed, #17 still something wrong, #18 would seem tolerable with maximum 4% (1/25).
My thought was to work backward from the actual battery current measurements to find the issue and how much is tolerable.
Nothing I can do to change the cells or battery IR. Just to look at cable length, connections and placement.
My thought was to work backward from the actual battery current measurements to find the issue and how much is tolerable.
Nothing I can do to change the cells or battery IR. Just to look at cable length, connections and placement.
Badgermonkey
New Member
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GRATS on making it this far before my pedanticism. Start a "Math for Smarties" thread?
What would be the typical IR for the batteries, and the resistance of the busbars between two adjacent batteries?
RCinFLA
Solar Wizard
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A good bus bar to terminal surface clamping interface resistance is 0.04 to 0.08 milliohm. Poor terminal connection can be much greater. Making low resistance cell terminal connections is one of the common issues with DIY'er construction. Aluminum cell terminals quickly grow aluminum oxide surface coating which is non-conductive.
Typical copper core bus bars, 72 mm terminal to terminal spacing length, 20 mm wide, 2 mm thick, are 0.04 to 0.05 milli-ohms depending on nickel plating thickness. If you are unfortunate to get stuck with brass core bus bars, they are 4x the resistance of copper.
As to battery, it depends on what you are calling cell IR. Larger AH size cells usually have lower metal and metal interface resistivity within cell. Static IR cell resistance for 280 AH EVE-like cell is 0.15 to 0.25 milliohms. This is primarily just terminal to layer foil metal conductivity and interface between metal foil and cell electrode material (graphite & LFP). It also contains a small amount resistance due to electrode material and electrolyte conductivity. It is what you measure with a 1 kHz battery impedance tester.
Under load current, I*R_static of cell resistance does not include cell voltage slump due to overpotential for lithium-ion migration. This voltage slump has an exponential time decay to equilibrium voltage which takes about 60-180 seconds to reach 99% of final equilibrium cell voltage value. The overpotential voltage slump is proportional to logarithm of cell current, getting larger in value for greater cell current.
In small to moderate cell current range, <0.4 C(A), this overpotential voltage slump is much greater than voltage drop due to cell I*R_static resistance. At very low cell current there is 10-20 millivolt overvoltage from rested unloaded cell voltage which is why just paralleling cells will not fully balance their state of charge.
I have to use actual resistance values to make calculations, so if I attribute .06 milliohms to the clamping resistance, doubling because there are 2 of them, that's .12 milliohms. Add .05 milliohms for the bar resistance, I get .17 milliohms for the total link resistance. If the battery static IR is .25 milliohms, doubling that to account for reaction resistance gives .50 milliohms for the "effective" battery IR.
Setting battery IR to .50 milliohms, .17 milliohms for link resistance, and with 100 amp load current, the calculation gives these theoretical battery currents in amps for a 6 battery parallel string, with the standard diagonal connection (load connection at the extreme diagonal corners):
Example 19
28.2
13.7
8.14
8.14
13.7
28.2
That's not so great. If I reduce the link resistance to .010 milliohms, the theoretical battery currents in amps are then:
Example 20
17.7
16.5
15.8
15.8
16.5
17.7
The low IR of modern batteries requires very low link resistance to achieve good balance. To achieve a link resistance of .010 milliohms would be very difficult, but this theoretical calculation shows that even if we could do so, the balance would still have room for improvement.
Now let's reset the link resistance to .17 milliohms and move the load connections away from the very ends of the string to the next battery terminal toward the middle, doing this at both ends of the string. Now I get these theoretical battery currents in amps:
Example 21
13.7
22.7
13.5
13.5
22.7
13.7
This is well worth doing (compare to example 19)! But it's still not great.
If I leave the load connection as in Example 21, and reduce the link resistance to .010 milliohms, these would be the theoretical battery currents in amps:
Example 22
16.5
17.1
16.4
16.4
17.1
16.5
Setting battery IR to .50 milliohms, .17 milliohms for link resistance, and with 100 amp load current, the calculation gives these theoretical battery currents in amps for a 6 battery parallel string, with the standard diagonal connection (load connection at the extreme diagonal corners):
Example 19
28.2
13.7
8.14
8.14
13.7
28.2
That's not so great. If I reduce the link resistance to .010 milliohms, the theoretical battery currents in amps are then:
Example 20
17.7
16.5
15.8
15.8
16.5
17.7
The low IR of modern batteries requires very low link resistance to achieve good balance. To achieve a link resistance of .010 milliohms would be very difficult, but this theoretical calculation shows that even if we could do so, the balance would still have room for improvement.
Now let's reset the link resistance to .17 milliohms and move the load connections away from the very ends of the string to the next battery terminal toward the middle, doing this at both ends of the string. Now I get these theoretical battery currents in amps:
Example 21
13.7
22.7
13.5
13.5
22.7
13.7
This is well worth doing (compare to example 19)! But it's still not great.
If I leave the load connection as in Example 21, and reduce the link resistance to .010 milliohms, these would be the theoretical battery currents in amps:
Example 22
16.5
17.1
16.4
16.4
17.1
16.5
That's better than 4/0 gauge cable! A 72mm link of that would have a resistance of .001 milliohm; that's 1 microohm! In such a case I suspect that the clamping resistance will dominate the overall link resistance.
If I set the link resistance to .081 milliohms battery IR to .50 milliohms and load current of 100 amps, here are the theoretical battery currents in amps for the standard diagonal connection:
Example 23
23.5
15.1
11.4
11.4
15.1
23.5
Let's move the load connections away from the very ends of the string to the next battery terminal toward the middle, doing this at both ends of the string. Then the theoretical battery currents in amps are:
Example 24
15.1
19.9
15.0
15.0
19.9
15.1
The trick that worked with the 4 battery and 3 battery parallel string of making the load connection to the link partway between the battery terminals as in Example 9 and Example 15 doesn't completely give perfect balance for the 6 battery parallel string, but it does change things. I'm going to research whether making the connection at some point other than 50% or 33% of the way along the link is better.
If I make the connection 50% pf the way along the links as in example 9, here's what I get for the 6 battery parallel string. The battery IR is .50 milliohms and the link resistance is .081 milliohms here are the theoretical battery currents in amps:
Example 25
19.3
17.5
13.2
13.2
17.5
19.3
All these calculations I've done make the point that with batteries connected in a parallel string, lowering the battery IR makes the balance worse, but lowering the link resistance makes it better. Since higher battery IR makes the balance better, one could artificially increase the battery IR by adding a length of cable between the battery terminals and the busbar. This will waste some energy in heating up the the added cable resistance, but it might be worth the tradeoff in better balance.
Have you measured the currents of the individual batteries under load? It's possible to work the problem backwards and calculate what the battery parameters such as IR must be to give the measured currents.
I've done some further research and I found another way to achieve perfect balance for parallel battery strings of 3 and 4 batteries.
In post #4 I showed a method to achieve perfect balance that is most practical in a setup with busbars because the method requires making the load connection partway along the busbar between two batteries. This is much more practical than trying to make that intermediate connection on a link cable.
Another method is to use the standard diagonal connection of, for example, 3 batteries, but change the resistance of the links. This method will be most practical when the links are lengths of cable rather than busbar. The IR of the batteries must be nominally identical as in the other perfect balance connections. The image below shows the resistance of the links in orange beside the links. R simply means whatever resistance a typical cable link the user would ordinarily use in this connection. 2R simply means a cable of twice the resistance; just making the cable twice the length of a cable of resistance R would do the job except that the clamp resistance of the lugs complicates things somewhat. But if the lug clamp resistance can be taken into account and a link resistance of 2R is manufactured, the theoretical perfect balance will be achieved.
This connection gives theoretical perfect balance which does not change with changes in battery IR as long as the IR of the batteries remain the same with changes in temperature, SOC, etc. The balance also does not change for different link resistance as long as the resistances of the links remain in the ratio shown in the image.
The same method works with the 4 batteries in parallel string. The balance is achieved by increasing the resistance in the path for the current supplied by battery numbers 1 and 4. As shown in the image, the resistance of two of the links is increased to 3 times the resistance of the other links. So if the links labeled "R" have a resistance of .1 milliohm, the links labeled "3R" will have a resistance of .3 milliohm. This can be accomplished approximately simply by making the links labeled "3R" three times longer than the links labeled "R". More accurate work will take into account the lug clamping resistance. One could also accomplish this by using smaller cable of the appropriate length for the links labeled "3R".
The actual resistance of the links doesn't matter (has no effect on balance) as long as the ratio of the link resistances is as shown in the image below. This property of the connection means that the (cable) link resistances could be higher than one would use with busbar at the expense of greater heating of the links. This tradeoff of greater energy loss versus smaller cable size and lug size could be a useful tradeoff if really low cable resistance would mean lugs too large to fit the battery terminals; Will ran into this problem in one of his videos.
In post #4 I showed a method to achieve perfect balance that is most practical in a setup with busbars because the method requires making the load connection partway along the busbar between two batteries. This is much more practical than trying to make that intermediate connection on a link cable.
Another method is to use the standard diagonal connection of, for example, 3 batteries, but change the resistance of the links. This method will be most practical when the links are lengths of cable rather than busbar. The IR of the batteries must be nominally identical as in the other perfect balance connections. The image below shows the resistance of the links in orange beside the links. R simply means whatever resistance a typical cable link the user would ordinarily use in this connection. 2R simply means a cable of twice the resistance; just making the cable twice the length of a cable of resistance R would do the job except that the clamp resistance of the lugs complicates things somewhat. But if the lug clamp resistance can be taken into account and a link resistance of 2R is manufactured, the theoretical perfect balance will be achieved.
This connection gives theoretical perfect balance which does not change with changes in battery IR as long as the IR of the batteries remain the same with changes in temperature, SOC, etc. The balance also does not change for different link resistance as long as the resistances of the links remain in the ratio shown in the image.
The same method works with the 4 batteries in parallel string. The balance is achieved by increasing the resistance in the path for the current supplied by battery numbers 1 and 4. As shown in the image, the resistance of two of the links is increased to 3 times the resistance of the other links. So if the links labeled "R" have a resistance of .1 milliohm, the links labeled "3R" will have a resistance of .3 milliohm. This can be accomplished approximately simply by making the links labeled "3R" three times longer than the links labeled "R". More accurate work will take into account the lug clamping resistance. One could also accomplish this by using smaller cable of the appropriate length for the links labeled "3R".
The actual resistance of the links doesn't matter (has no effect on balance) as long as the ratio of the link resistances is as shown in the image below. This property of the connection means that the (cable) link resistances could be higher than one would use with busbar at the expense of greater heating of the links. This tradeoff of greater energy loss versus smaller cable size and lug size could be a useful tradeoff if really low cable resistance would mean lugs too large to fit the battery terminals; Will ran into this problem in one of his videos.
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Can your mathematical model confirm that wiring each battery to a common bus bar, using equal length cables to each battery, provides a balanced charge/discharge?
HighTechLab
AKA Dexter - CTO of Current Connected, LLC
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How could you do it with busbars, using5 batteries in a server rack, for example the SOK server rack with an extra battery set right on top of the top battery (with spacer to make it evenly spaced in relation to the other batteries)?
I think the busbar with slightly inset connection point no longer works in that scenario...Also the "halfway" using cabling. Does this example/method cap out at 4 batteries?
I think the busbar with slightly inset connection point no longer works in that scenario...Also the "halfway" using cabling. Does this example/method cap out at 4 batteries?
Have a look at post #25 (also see post #4). The right hand part of the image shows 4 batteries connected to a common busbar with equal length cables. Whether or not it gives a balanced charge/discharge depends on how the load is connected to the busbars. If the load is connected as shown by the red/black load cables, the balance will not be perfect, although it can be quite good if the busbars are thick, low resistance items. If the load is connected as shown by the yellow/blue load cables, the balance can be perfect provided that the IR of the batteries are identical.
It's also possible to get a perfect balance with 3 batteries in parallel if the proper load connection to the busbars is made.
I haven't been able to find a load connection to the busbars giving perfect balance with 5 or more batteries in parallel, but I'm still searching for one.
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I haven't found a perfect balance connection for 5 or more batteries in parallel, but the method does give improvements for those cases. I'll post some of my findings about those higher number strings before too long.
I've been following the thread since the beginning. The configuration I'm asking about is a little different. Is it effectively different? I don't know.
What I'm talking about is a small bus bar with all cables connected to it. The studs on the bus bar are no more than 1.5" apart. Despite my lousy diagram below, the cables are all equal length. Maybe I'm asking a question for which the answer is simply obvious, that the balance is as good as you can get.
Your diagram shows only one wire connecting to the red busbar where I've shown a blue dot. Surely you have 4 wires connected to 4 studs on the busbar I've shown as 4 big black dots; is that correct? Could you also show where your load cable is connected to the red busbar?
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Your diagram shows only one wire connecting to the red busbar where I've shown a blue dot. Surely you have 4 wires connected to 4 studs on the busbar I've shown as 4 big black dots; is that correct? Could you also show where your load cable is connected to the red busbar?
It was a quick-n-dirty PowerPoint drawing. In my description I noted that the connections were 1.5" apart, which is pretty close to what you added.
Could you indicate on my drawing where the load is connected? Is it connected in the middle or at one of the ends of the busbar?
I've done some calculations on a 5 battery parallel string and here are my results.
I'm using a value of 1 milliohm for the battery IR, and .1 milliohm for the link resistances which I think is more representative of what one gets with busbars rather than cable links. The load current is 100 amps. I'll reference this image:
The red and black load connections are the standard diagonal connection, and that connection gives me the following theoretical battery currents in amps:
Example 26
23.5
18.2
16.6
18.2
23.5
Some have suggested moving the load connection toward the middle of the string. If the black load connection is moved to the point on the busbar adjacent to the negative terminal of battery 2, and the red load connection is moved to the point on the busbar adjacent to positive terminal of battery 4, we get these theoretical currents in amps:
Example 27
18.3
21.8
19.8
21.8
18.3
This is a substantial improvement. In some of the earlier hookups it was possible to get a perfect balance by connecting the load to the right place on the busbars between the last and next to last batteries in the string. Of course, I have tried to do that for this 5 battery string by varying the connection point. It isn't possible to get perfect balance, but it is possible to get improvement. I had to consider how to measure the improvement, and what seems reasonable is to get the least variation in the battery currents. I had my calculations include the standard deviation of the battery currents, and tried all the connections between the end batteries and the next-to-the-end batteries in 5% increments. For this 5 battery string, the connection which is 60% of the way from the last battery to the next battery inward gives the minimum variance in the battery currents. This would be a connection like the yellow/blue connection shown in the image above, at the 60% point. Here is the result of the 60% connection theoretical battery currents in amps:
Example 28
20.3
20.4
18.5
20.4
20.3
I haven't given up on the possibility of a perfect balance for this string, but no joy so far.
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To keep it simple, let's assume that the load is in the middle. Reality is a bit more complicated as my bus bar has two rows of studs, so batteries are connected on one set of studs and all load/charge devices are on the second row. The Blue Sea Bus Bar is one solid piece of copper. Even that's not how I have it wired at this time, but it's close enough.
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