Connecting cells in series and then parallel or opposite

I want to connect 26 Li-ion 2170 cells to create a 48 V power source.

I can do it in two ways:

1. Connect 13 cells in series (to obtain ~48 V) and then connect two such packs in parallel.
2. Connect cells in pairs in parallel, and then connect 13 pairs in series.

Which way should I use and why?

I found this answer that suggest that the way (1) is safer (but the question was about lead-acid batteries, I am not sure if it applies to Li-ion too).

On the other hand, Tesla connects the cells in parallel first and then in series. (quora, reddit), which is the way 2.

• (Parallel first would seem somewhat common for shared supervision&balancing circuitry.) Commented Jan 2, 2023 at 23:12
• Could you please elaborate on that? Or give some resources to learn.
– hans
Commented Jan 2, 2023 at 23:13
• (Look for terms like 7S4P to 13S10P, with 10S7P in middle ground. (Configurations of cells, 7 series of 4 parallel to even bigger batteries. (Yours may be 13S2P and 2P13S, respectively - if only I didn't forget which is which.)) Should take you to fori about functional models or "e-bikes"/pedelecs or whatever, with a lot of opinions about batteries and supporting electronics. The communities I frequented don't communicate in English. What I found on EE@SE was unimpressive.) Commented Jan 2, 2023 at 23:37
• The series-first arrangement can be useful with cells which tend to fail short, which is not how Li-ion cells usually age. Commented Jan 3, 2023 at 8:19
• What is usual Li-ion cells failure mode, increased internal resistance?
– hans
Commented Jan 3, 2023 at 10:02

Short:

Using 13 sets of 2 cells in parallel would be the usual choice in all but very specialised applications.

13s x 2 strings is arguably slightly more 'by the book' than a 13s combination of parallel cell pairs. If you were implementing eg a Mars Rover you might choose that method. However, practical implementation aspects would mean that paralleling pairs of cells would usually be chosen.

A 13s LiIon battery requires a BMS which ensures per cell balance.

If you combine two seperate 13s strings you will need a 13s BMS for each string. If you parallel cell pairs you then require only a single 13s BMS. Paralleling cell pairs saves a 13s BMS and in practice has reasonable success if the cells are identical and well balanced initially.

Paralleling two cells demands that the cells are first well balanced with respect to each other. This may be achieved by first individually conditioning each cell by a method that ensures they are both in an equal state, or by joining the two with a suitable resistance value such that they mutually charge or discharge to a common voltage. The latter method is easier but can in fact lead to a degree of imbalance. (eg two cells may both have a 4.2V terminal voltage but be at eg 85% and 100% state of charge.

If cell pairs are paralleled it is usual to individually fuse each cell, usually from the common bus. This can easily done by using a short length of suitable sized wire from one cell terminal to the bus. This fuse is dimensioned to blow only in extreme overload conditions - usually such as occurs due to a cell failure which might otherwise catastrophically destroy the whole battery. Such a failure will immediately halve the effective capacity of the whole battery.
An adequately intelligent BMS will be able to identify this failure and provide an alarm condition.
A minimum function BMS may attempt to balance the single cell relative to the rest of the battery. Most BMSs have limited balance capacity range and will fail - either to an alarm state or to a catastrophic failure.
A battery with two separate 13s strings will also lose half capacity if one cell-fuse blows BUT does not suffer from the parallel cell failure mode described above.

A very specialised approach (which I've not heard of in practice) would be a BMS that removed a cell or cell pair if they fail. This then gives either s x 12S strings or a 12s string of parallel pairs.

• A 13s string using a 3V to 4V2 cell voltage range has a battery voltage range of 39 to 54.6V.
• A 12s string has a 36 to 50.5V range.

Using only voltage as a metric the 12s battery has 11.4v range and the 13 s has a 14.4V range. Allowing for very little energy below 3.1V/cell and reduced energy at the bottom and top of the remaining range, as 12S good condition battery may still be superior to a 13s battery in either configuration with one cell fuse blown.

In many applications where the battery supplies a voltage converter with a wide range of acceptable voltages a 12s battery will have 12/13 = 92% of a 13s battery. Most VMSs will not allow a cell or cell pair to be bypassed, but in specialised enough applications it may be worthwhile.

• Excellent answer, thank you! Could you elaborate a bit about fusing? AFAIU, in case of n cells in a parallel group I need n fuses. If I had only 2 cells in parallel and 2 fuses, any can activate resulting in two possible states: battery A is short and disconnected or battery A is short, but battery B gets disconnected. right?
– hans
Commented Jan 3, 2023 at 9:55
• Probably the above comment should be a separate question.
– hans
Commented Jan 3, 2023 at 10:04
• @Hans What causes fuses to blow with parallel cell pairs in a series string is 'an interesting question'. || For A&B in parallel I confidently started to describe what happens if eg B goes short and realised it depends on a number of factors including effective resistance of B, normal string current into load and more. Needs thought. Asking it as another question may in fact be useful. With >=3 cells in parallel you can probably expect the shoted cell's fuse to blow. With 2 in parallel it looks interesting. Commented Jan 4, 2023 at 9:29

There's only one effective way to connect them: parallel first (make a block of cells in parallel, then connect blocks in series).

1. The battery will perform better in case of weak cells
2. A BMS for it is far cheaper and more available

3.5.1 Disadvantages of series-first

The series-first arrangement is problematic due to its many disadvantages.

3.5.1.1 Higher cost

Often, people new to battery design envision a battery with a large number of strings in parallel; after they recover from the shock of the price and complexity of a BMS for that arrangement, and after they are told the advantages of the parallel-first arrangement, these designers usually reconsider their plan; in the end, they are pleasantly surprised by the significantly lower cost for a BMS for a parallel-first arrangement 98. The series-first arrangement is more expensive than parallel-first because it uses a more complex BMS; for example, a 3P4S battery requires a BMS with five taps (fig. 3.39a), while a 4S3P battery requires a BMS with eleven taps (fig. 3.39b). This disadvantage grows as the number of strings increases; for example, a 10P10S battery requires a BMS with eleven taps, while a 10S10P battery requires a BMS with 92 taps!

A BMS that can handle strings in parallel is rare. Using ten separate BMSs is not practical because they cannot be easily coordinated to work as a single BMS. It may be tempting to combine the tap wires from all the cells in a row through resistors that give the BMS the average voltage of all the cells in one row (fig. 3.39c). While this would reduce the number of taps, it does not work:

• With ten cells in parallel, if one is down to 0 V and the others are at 3.5 V, the average voltage is 3.15 V, which is acceptable to the BMS, which has no idea that a cell is in such a bad shape (As I write this, I quoted a BMS for a 10S60P battery at $9000; rearranging the same cells to 60P10S brought the price down to$ 800.)
• With two cells, one at 5 V and one is at 2 V, the average is 3.5 V; the BMS has no idea that one cell is way over- charged and the other is way over-discharged
• Balancing is impractical because of these resistors
• The BMS reads the wrong voltage because the small current into the BMS sensing input results in a small voltage drop across the resistors

3.5.1.2 Worse performance

In the real world, cells have variance and a few cells may be weak in that they have a lower capacity and/or a higher resistance. By connecting cells directly in parallel, the cells in parallel with the weak cell will “help carry its weight” and will reduce its effect on battery performance.

If low capacity cells are distributed randomly in a battery, the capacity will be higher with parallel-first (fig. 3.40b) than with series-first (fig. 3.40c).

Similarly, if high resistance cells are distributed randomly in a battery, the resistance will be lower with parallel-first (fig. 3.41b) than with series-first (fig. 3.41c).

Granted, a single high resistance cell won't affect the total resistance of the battery as much as a low capacity cell would.

The voltage of a high resistance, weak cell will swing significantly under load; the BMS will shut down the entire battery when a weak cell's voltage exceeds the limits, even though the other strings are OK:

• With no load current, all the cells are at 4 V and the total voltage is 16 V (fig. 3.42a)
• Under 100 A load current, the BMS shuts down the battery (fig. 3.42b):
• The center and right strings carry practically all of the current (50 A each) and the voltage of their cells drops down to 3 V; the total voltage drops to 12 V
• The leftmost string carries little current because of the weak cell; because they are carrying practically no current, the good cells in that string remain at 4 V, for a total of 12 V; that leaves 0 V across the weak cell's terminals, which it is unable to overcome through its high resistance
• The BMS sees that the voltage on the high resistance cell dropped to 0 V, and shuts down the battery

• Perfect, thank you for breaking it down to different failure scenarios. Did you create the figures or they come from a book? If the later, could you possibly provide the reference?
– hans
Commented Jan 3, 2023 at 10:00
• Did you create the figures or they come from a book? Yes and yes. Commented Jan 3, 2023 at 12:46
• There are a couple of numbers in your answer (98 twice, 163) that don't appear to be intended to be numerical values - perhaps intended to be some form of cross-references to some other resources? Commented Jan 3, 2023 at 15:24
• Oh, those are callouts to footnotes and page numbers. Sorry. I fixed it. Thank you. Commented Jan 3, 2023 at 16:00