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Series and Parallel Cell Configurations

I do not claim to know everything there is to know about battery packs, but from building my fair share of packs, I am hoping to pass on a bit of knowledge.

In order to build a battery pack, individual cells must be configured in series and parallel configurations to achieve greater capacity and voltage.
Each cell has a certain capacity, voltage, and max current that can be determined from the cell’s datasheet. If a datasheet cannot be found, a general safe rule for 18650 style cells is a 1C (1 times the cell’s capacity) discharge rate.
There are a few basic rules to remember.

Parallel Connections:

Achieved by directly connecting the positive ends together and the negative ends together (+ to +, – to -).
Capacity of the cells are added together to achieve a higher capacity battery.
Voltage of the cells remain the same.
Before connecting all the cells together, be sure that all cells are at the same voltage (within 0.05V). If there is a large voltage difference between the cells, when you connect them in parallel with a wire (0 ohm resistance) then when connected together, the cells will try to balance out the voltage. With a larger voltage difference, the current flowing between the cells to balance them out will be large – and charging li-ion cells quickly will create heat.
Cells connected in parallel act as a single, larger capacity cell.
Another common question with parallel cell connections is if connecting cells with different capacities will be problematic. This in fact is not a problem. When discharging the cells with different capacities in parallel, the cell with higher capacity will discharge at a higher current in order to keep the voltage between the cells the same. If both cells discharged at the same rate, the cell with lower capacity would drop voltage quicker. Since the cells are parallel the voltage on each cell must be the same, so discharging cells at the same rate does not work. Both cells must maintain the same voltage, so the cells must discharge at different rates relative to their capacities.

Series Connections:

Achieved by connecting the positive end of one cell to the negative end of the next (+ of Cell 1 to – of Cell 2).
Capacity of the cells remain the same.
Voltage of the cells is added together.
Before connecting cells in series, it is advised but not necessary to balance the cells. The main drawback to connecting cells in series is that the cells must always be monitored to keep avoid over-discharging or over-charging individual cells.
The cells that are chosen to connect in parallel must ideally have the same capacity, age, and internal resistance (capacity is the most important) so that when charging the pack, the cells do not become unbalanced. When charging the pack, if one cell has a lower capacity than the rest, that cell will reach full charge before the others, but the battery will not be at a full charge voltage yet, so it will keep charging. The cell with a lower capacity will now be overcharged and risk heating up and going into thermal runaway. A similar thing will happen when discharging – the cells with a lower capacity will be discharged to a lower voltage than the rest and could be over-discharged if not properly monitored.
Because of this, it is strongly advised to have a Battery Management System (BMS) that is able to monitor the voltage of the pack and prevent over-discharging or over-charging cells. Higher end BMS systems will also include cell balancing – they will keep all the cells at the same voltage level either by bleeding off the extra energy in the high capacity cells through discharge resistors as heat (passive balancing), or by transferring charge of the high capacity cells to the low capacity cells through transformers or other methods (active balancing). Active balancing is generally the better option, as it does not waste excess energy, but it is more expensive to implement.

Naming:

A battery with X cells in parallel and Y cells in series is referred to as XPYS.
So a battery with 3 cells in parallel and 2 cells in series is referred to as 3P2S.
This battery has 6 cells in it with 3 in paralled, and 2 of those parallel groups in series. It has 2x the voltage and 3x the capacity of a single cell.

2S3P

3P2S

The order of the P and S designations in the battery can mean different things. I have heard differing opinions on about whether this 2S3P battery is the same as a 3P2S battery. Both batteries will contain 6 cells, but the order of how they are connected will differ slightly. A 2S3P battery will have 3 series strings of 2 batteries connected in parallel, while a 3P2S battery will have 2 series sets of 3 cells in parallel. The main difference with the 2S3P battery would be that there is no parallel connection across the first set of 3 cells. Each series string of cells should have its own BMS, as all 6 cells could be at different potentials (voltage). It is advised to go with a large parallel group of cells, and put those large parallel groups in series if possible, unless there are problems implementing such a system. When connecting multiple LiPo batteries in parallel through their power connectors, each individual cell should be monitored, as this is a 2S3P style system. A modular battery pack might also make use of this design so that some cells can be removed, while still maintaining the correct voltage to operate whatever device it is powering. The naming and the advice here are not strict rules, but just some of what I have come across on my extensive battery building journeys.

If interested in more information on lithium batteries, here is a great article.
It leans more towards information on charging and storage safety for LiPo batteries, but has tons of great information.