Attaching sense wires in large modular batteries

The easy case: bicycles

A BMS is supposed to keep track of each and every cell group's voltage. In bicycles, this can be easily solved with n+1 wires, where n is the number os cell groups in series. This is why the BMSs we buy from China have 11 wires for 10S, 14 wires for 13S, etc.

However! For this to be the case, we need to assume that:

V_B1+ = V_B2-
V_B2+ = V_B3-
...

That is, that the resistance of the connection between the cell groups is much less than the internal resistance (IR) of the cells. This is true for bicycle batteries that looks something like this:

Typically a good 18650 cell would have a discharge IR of between 50 and 100 mOhm. Therefore 4 in parallel, as on the photo above, will have something like 10-20 mOhm.

Welding is a very efficient, very low contact resistance connection method. Nickel is a very good conductor, and the current path is very short. The resistance is in the microOhm level. Therefore the above assumption is valid.

The hard case: modular batteries

When for space or other considerations it is not possible to simply put the cells side by side and weld them, the contact resistance starts playing a role. Take for example the Buddy car battery, which is a 20S145P configuration. The IR would be ~0.7 mOhm.

The voltage drop on a cell groups at 300 A would be:

V_drop = 300 A * 0.7mOhm = 0.21 V

This is barely below what we see on a cell group when the sense is directly connected to positive and negative busbar. This is because the resistance of the busbar is negligible, and the bus bar is soldered and welded to the cell terminals.

Meanwhile, the modules are connected in series by busbars, screwed together ring terminals,  and 4AWG crimped copper wire. In practice, we see a voltage drop of 0.35 V, in some cases even 0.5 V.

Look at the below schematic of a 2S design to understand how the resistances are connected, and where the sense is. The values are approximate.