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Battery Capacity Math Question
#1
I am unclear on several battery capacity concepts and I hope someone can help me clear them up.


Example 18650 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?
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#2
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 Smile
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#3
(09-05-2020, 04:56 PM)daromer Wrote: 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 Smile


Thanks very much for the reply.  It should all be mAh.
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#4
(09-05-2020, 04:26 PM)zensane Wrote: 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. [...]

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 pack at 3A for 1h = 3Ah (50%) total. Because the 4Ah cell has half the IR of the 2Ah cell it supplies twice the current, so the 3A pack discharge current splits as 2A from the 4Ah cell and 1A from the 2Ah cell. So our 1h discharge drains 2A * 1h = 2Ah (50%) from the 4Ah cell, and 1A * 1h = 1Ah (50%) from the 2Ah cell,  leaving both 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.
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#5
(09-05-2020, 05:48 PM)gauss163 Wrote:
(09-05-2020, 04:26 PM)zensane Wrote: 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. [...]

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).

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 remain the same in a 2p battery, I don't understand how the current at the cell level can vary between cells of the same voltage unless resistance is also changing.  Does resistance in a cell change with the current?
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#6
Moved to proper location. This isn't a Project status report but asking about build design. Please keep threads in their appropriate sections.
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#7
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.
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#8
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.
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#9
(09-08-2020, 01:00 PM)Overmind Wrote: So to increase voltage, put more in series, to increase current and capacity, put more in parallel.
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 changing each 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 Smile
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#10
(09-08-2020, 03:06 PM)OffGridInTheCity Wrote: [...] 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

No, standard English terminology is that battery "capacity" refers to its charge capacity (Ah). Instead, what you refer to is called energy (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 series string, 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).
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