Battery Capacity Math Question

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zensane

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I am unclear on several battery capacity concepts and I hope someone can help me clear them up.


Example18650 Battery:
Voltage: 4v (for quick math)
Max charge: 1 amp
Max discharge: 3 amp
Capacity:2000 mAh


4s:
Voltage:16v
max charge: 1 amp?
max discharge: 3 amp?
capacity: 2000 mAh?

4p:
Voltage: 4v
max charge: 4 amp?
max discharge: 12 amp?
capacity: 8000 mAh

4s4p:
Voltage: 16v
max charge: 4 amp?
max discharge: 12 amp?
capacity: 8000 mAh?

4p Question:
battery 1: 2000mAh
battery 2: 2000mAh
battery 3: 1500mAh
battery 4: 2000mAh

It seems to me that battery 3 is going to cause an overcharge problem. It will reach 4.2v prior to battery 1,2,4. This would also not be managed by a BMS in a 4s4p scenario. I am using an extreme example, but I believe this would be the case even if the individual cells are only 50mAh apart?
 
If you have 4 cells in parallel they will always have the same voltage but they will get different amount of current during discharge and charge if they have unequal capacity.

The important thing here is that every pack in series is close to equal. If they arent they will reach different levels at different time. Thats why you top balance so you try to keep them level at the top charge when charged up. At bottom they will vary but.

1. You will more often reach full charge
2. Its more dangerous to over charge then over-discharge. Therefore more importan to top balance
3. Most BMS systems are made to top-balance.


Your numbers are a bit wrong. You mention Ah on the cells and mAh on the other so some zeros wrong. Except for that its correct.

Its mAh or Ah :)
 
daromer said:
If you have 4 cells in parallel they will always have the same voltage but they will get different amount of current during discharge and charge if they have unequal capacity.

The important thing here is that every pack in series is close to equal. If they arent they will reach different levels at different time. Thats why you top balance so you try to keep them level at the top charge when charged up. At bottom they will vary but.

1. You will more often reach full charge
2. Its more dangerous to over charge then over-discharge. Therefore more importan to top balance
3. Most BMS systems are made to top-balance.


Your numbers are a bit wrong. You mention Ah on the cells and mAh on the other so some zeros wrong. Except for that its correct.

Its mAh or Ah :)
Click to expand...


Thanks very much for the reply. It should all be mAh.
 
zensane said:
4p Question:
battery 1: 2000mAh
battery 2: 2000mAh
battery 3: 1500mAh
battery 4: 2000mAh

It seems to me that battery 3 is going to cause an overcharge problem. It will reach 4.2v prior to battery 1,2,4.[...]
Click to expand...

Batteries in parallel will always be at the same voltage (so same SOC if they have the same chemistry and temp, and the voltage is measured at rest).

Let's consider a simpler (ideal) example. Suppose we parallel a 4Ah and 2Ah cell of same chemistry, and the 4Ah cell has half the IR of the 2Ah cell. Starting at full charge we discharge this 2P 6Ah packat 3A for 1h = 3Ah (50%) total.Because the 4Ah cell has half the IR of the 2Ah cell it suppliestwice the current, so the 3A pack discharge current splits as 2A fromthe 4Ah cell and 1A fromthe 2Ah cell. So our 1h discharge drains 2A * 1h = 2Ah (50%) from the 4Ah cell, and 1A * 1h = 1Ah (50%) from the 2Ah cell,leavingboth at the same SOC so same rest voltage at the end of discharge (because the bigger cell drains faster). An analogous effect occurs during charge.

In practice it is more complicated:IR depends on SOC, temp etc, and chemistries may differ so V->SOC may differ,but the currents will always(instantaneously) adjust in a way that always keeps the voltages of the parallel cells the same - just as in the simple example above.
 
gauss163 said:
zensane said:
4p Question:
battery 1: 2000mAh
battery 2: 2000mAh
battery 3: 1500mAh
battery 4: 2000mAh

It seems to me that battery 3 is going to cause an overcharge problem. It will reach 4.2v prior to battery 1,2,4.[...]
Click to expand...

Batteries in parallel will always be at the same voltage (so same SOC if they have the same chemistry and temp, and the voltage is measured at rest).
Click to expand...

I am new to this entire subject with only a rudimentary electrical background. I think I understand what you are saying but I don't have the IR concept. I am going to have to read more on this. If you can point me in the right direction, that would be great.

V=I*R

If voltage and resistance remainthe same in a 2p battery, I don't understand how the current at the cell levelcan vary between cellsof the same voltage unless resistance is also changing. Does resistance in a cellchange with the current?
 
Moved to proper location. This isn't a Project status report but asking about build design. Please keep threads in their appropriate sections.
 
IR is the internal resistance of the cell.
You can't use a multimeter ohms setting to measure this.
The easiest way to measure it is with a 4-wire resistance meter like a YR1030 or similar.
It give a good indication of a cell's health.

IR affects how much heating occurs when charging & discharging + how efficient the charge/discharge is.
Bad &/or old cells have higher IR & it increases over the cells life.

Re max charge or discharge currents, this varies with the type of cell.
Some are designed for high currents, some designed for lower sustained currents.
Higher rates for any cell increase cell aging, lower currents extend cell life.
 
To remember in a simple manner:

Series add-up voltage, keep everything else the same.

Parallels add capacity and max current (for both charge and discharge) and keep voltage.

So to increase voltage, put more in series, to increase current and capacity, put more in parallel.
 
Overmind said:
So to increase voltage, put more in series, to increase current and capacity, put more in parallel.
Click to expand...
Yes - this is generally correct. However, a nit if I may..

You increase capacity when you add cells in series as well. For example...
2s (2 in series) of 2000mah cells =16wh. 4s (4 in series) of 2000mah cells = 32wh.

The reason you don't use 'series' as a technique to add capacity is that this would result in the voltage changingeach time you added capacity this way. When you add cells in parallel to increase capacity you can keep the voltage steady. Keeping the voltage 'steady' is required else you don't know what equipment to buy :)
 
OffGridInTheCity said:
[...] You increase capacity when you add cells in series as well. For example... 2s (2 in series) of 2000mah cells = 16wh. 4s (4 in series) of 2000mah cells = 32wh
Click to expand...

No, standard English terminology is that battery "capacity" refers to its charge capacity (Ah). Instead, what you refer to is calledenergy (Wh). Sometimes "energy" is called "energy capacity" but it should not be called "capacity" since that easily leads to confusion between charge (Ah) and energy (Wh).

So post #8 is correct: pack capacity (Ah) remains constant when you add or remove a cell/pack in series (assuming all have same capacity), but the pack energy (Wh) increases or decreases (resp.)

If you place mixed capacity (differing Ah) cells/packs in series then the capacity is the minimum of those in the seriesstring, so it may increase if you remove the minimum (the new minimum can either be the same or higher). In particular, the capacity can decrease while energy increases (by adding a lower capacity cell), and the capacity can increase while energy decreases (by removing a unique lowest capacity cell).
 
While I get your comment, and its a good point....
I'm talking "power capacity" by using 16wh vs 32wh as the metric of capacity in my comment. Here's a quote fromhttps://learn.adafruit.com/all-about-batteries/power-capacity-and-power-capability-"Power capacity is how much energy is stored in the battery. This power is often expressed in Watt-hours (the symbolWh)."

While the previousposter said "capacity" (without clarification) I think DIY'ers will often mean "how long can I run something" when they say capacity. In the sense of "how long will my battery run something" - adding cells in series will increase (power) capacity. :)
 
OffGridInTheCity said:
I'm talking "power capacity" by using 16wh vs 32wh as the metric of capacity in my comment. Here's a quote fromhttps://learn.adafruit.com/all-about-batteries/power-capacity-and-power-capability-"Power capacity is how much energy is stored in the battery. This power is often expressed in Watt-hours (the symbolWh)."
Click to expand...

No, as I explained above, you are talking about battery"energy" (or "energy capacity") (Wh), not "power capacity" (W). Of course it comes as no surprise that there are some (hobby) pages on the web where authors misuse standard terminology (whether by oversight or inexperience).

Below is an example of the standard terminology, from an nrel.gov FAQ onGrid-Scale Battery Storage.

nrel.gov said:
What are the key characteristics of battery storage systems?

Rated power capacity is the total possible instantaneous dischargecapability (in kilowatts [kW] or megawatts [MW]) of the BESS, orthe maximum rate of discharge that the BESS can achieve, startingfrom a fully charged state.

Energy capacity is the maximum amount of stored energy (inkilowatt-hours [kWh] or megawatt-hours [MWh])
Click to expand...

and excerpted from a page on eia = U.S. Energy Information Administration (my emphasis).

eia said:
In 2010, 7 battery storage systems accounted for only 59 megawatts (MW) of power capacity, the maximum amount of power output a battery can provide in any instant, in the United States [...] These observations consider both power capacity and energy capacity, the total amount of energy that can be stored by a battery system [...] At the end of 2018, 869 megawatts (MW) of power capacity, representing 1,236 megawatthours (MWh) of energy capacity, of large-scale battery storage was in operation in the United States
Click to expand...

9bTD7.png
 
What about mixing cells with similar mAh capacity rating, but different continuous max discharge ?
For eg , 3s6p with 100mAh difference between each cell in each parallel section, with a combination of
, lets say 5A and 20A continuous max discharge ?

Usually when testing IR, the lower the better, but if you dont have the spec sheet, how do you know if the cell
is just a new 5A max continuous discharge cell with 35mOhm IR, or an older, higher discharge 20A cell with an IR of 35mOhm ? If your max load is 12v/10A and your 3s6p pack has a capacity of 12v/12A( 6 x 2000mAh cells/p), would
there be any issues of overheating ?
 
Let's say you have 50% laptop cells with max discharge of 1a and 50% ebike cells with max discharge of 10a.

Case 1 - You discharge the overall battery at 1a (or less) / cell. This is perfectlyOK as you are not exceeded the least cell's max discharge.

Case 2 - You discharge the overall battery at 10a / cell. This is NOT GOOD as it will overwork the 1a cells... and the battery will not respond well. Besides strain/damage to the lower max discharge cells -I believeyou'll see a hugevoltage drop... the battery will just fail to keep up. and the load will probably fail to run. It might trip aBMS shut-off. *Others may help clarify here - but this case is *all bad*, and is to be avoided.

One part ofcell testing is to validate a workingdischarge value ahead of battery construction to ensure what they will support. Thenthe battery can be built with enough cells to ensure you don't overload the battery - be it powerwall (typically low discharge/cell)or ebike (typically high discharge/cell).
 
If you know you have ebike batts vs laptop build different strings instead. And then paralelel. You still need to do what OffGridInTheCity said about looking at the minimal but doing above you atleast have some way dealing with them
 
Thanks for the info, Guys ! Thing is, i have no idea where these cells have been used.
Got given a box with various 400 x 18650s. Definately gotta check the cell database specs, to get some
idea about capacity/SoH/IR before "destroying" those that dont cut it.
 
UncleZeb said:
Thanks for the info, Guys ! Thing is, i have no idea where these cells have been used.
Got given a box with various 400 x 18650s. Definately gotta check the cell database specs, to get some
idea about capacity/SoH/IR before "destroying" those that dont cut it
Click to expand...
I'd recommend you test the cells yourself before using them. Here's a thread on 'testing' -https://secondlifestorage.com/showthread.php?tid=9560&page=6&highlight=Cell+Testing - that works to highlight a test process. Its basically charge/discharge at least 1 amp each cell to get its capacity - looking for 80-100% capacity compared to 'new'specs. Note I'm talking capacity rather than max discharge amps. Then let sit for a few weeks to make sure they don't self-discharge. Then,you can build a battery with good confidence that the cells will perform 'close to' original max discharge specs- but again its good toverify that the batteryperforms to your needs before you call it 'a wrap' :)
 
That link to the "Testing Thread" had some good pointers ... quality. Cheers Guys !
Fortunately, each cell had a voltage of range of min 2.65v(about 20-25cells) to 3.81v (nominal 3.62v), and IR ranging from
35m? ---> 142m? (Initial internal impedance ? 35m?)

What about certain cells that have IR over 100m? but SoH between 80-85%. No hope for them, as theyre
on their way out ? Anything under 80% is going in the bin.
 
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