With 3 x LiPo in series and no load connected, charging them one at a time is entirely acceptable.
- Note that LiPo and std LiIon are essentially the same for the purposes of this question. Key differences may be the maximum allowable charge rate as a proportion of full capacity. Std LiIon is usually charged at C (1 hour rate, ma = mAh capacity numerically) initially. Some few may allow 2C and some want as low as C/2 but usuallyy C. LiPo vary to some extent with manufacturer's boldness and higher rates may be allowed. See data sheet in all cases !!!
The charger need to be truly floating with respect to the battery when disconnected so that any one cell can be accessed at a time without interaction.
You would want to avoid having to use the combination while batteries were in a different state of charge - although even this would do no harm as long an no cell was discharged fully. The danger in discharging a series LiIon battery combination with different states of charge is that exhaustion of any one cell is not readily detected without monitoring each cell individually. If you DO monitor each cell for minimum voltage on discharge and stop discharge when this occurs, then even discharging a differentially charged battery is acceptable.
As you are going to need to connect to the cells one at a time, you could consider making up a switchable connection to the charger, and then rotate between charging cells reqularly. The excessively enthused [tm] could could easily automate this with eg relays (or electronic switches if more venturesome.)
Swapping between cells every few minutes say should still produce an acceptable charging pattern due to the well behaved nature of Lithium chemistry cells when charging (as opposed to eg NimH where this would be a bad idea. For the first 70%-80% of charging from fully discharged the call is in constant current more and then changes to constant voltage, decreasing current when maximum voltage is reached. Both these stages would be well handled even if you swapped batteries every few minute.
Parallel charging with a single cell charger is not possible without isolating the cells electrically. If the charger is not capable of providing more than Imax for any one cell then there would be little advantage in doing so compared to the occasional rotation method mentioned above.
If the charger was capable of providing say 3 x Imax then parallel charging would be faster than one at a time BUT current balancing would be absolutely essential.
There are very expensive $250- $300 chargers that do higher than 6s, probably closer to 10s, but not a lot to choose from and right now my memory is drawing a blank on their names, but they do exist.
I have no idea why there are not more, but I suspect that the demand is simply not there yet. Lithum batteries at those higher voltages are not as common and can be very expensive as are they chargers.
The charger you link to balances its battery by having a charging connection and balancing connection at the same time. The charging connection is directly connected to the + and - of the battery and supplies the main charge. The other connections are more complicated and, for example, in a 6s battery there would be 7 connections, one at the "-", on at the "+", and a connection or wire coming from every single cell connection. So each time another cell is added to make it a 2s or 3s, a wire comes out between the "+" and "-" of each cell added. So a connection between all 6 cells and one at the botom or "-" and one at the top or "+" and you have 7 wires coming out that will then plug into the side of the charger.
The charger then monitors each individual cell's voltage as it is charging the battery as a whole, but most chargers don't seem to start balancing until the battery is essentially full, or at least one cell is at 4.2 volts. Then it uses the seven wire connection to balance the battery, usually by discharging the higher voltage cells a little via a small current, and then charging the whole battery again slowly. Then repeat until all balanced.
It looks like what you linked to would work, except that they are for smaller number of cells in series than what you want to do.
Another option that would work for you is to do what you are doing - split the 10s into 2 5s and charge them independently, but parallel charge them using a parallel charging board and then you could charge them at the same time.
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Best Answer
The cell balancing is performed by a specific circuit a BMS (battery management circuit). Balancing allow to protect a lowest cells from venting and thermal runway. Your configuration is 25S4P, so using a BMS to control current and voltage is the best solution. If you use 100 single cell charger, it will be difficult to control them, since they have different Stat of charge, so the weakest will be rapidly damaged.