Series and parallel cells
A battery pack is built from identical cells:
- cells in series (S) add their voltages;
- cells in parallel (P) add their capacities and current capability.
A “13S4P” pack has 13 groups in series, each made of 4 cells in parallel: 52 cells in all.
The formulas
- Pack voltage = S × cell voltage
- Pack capacity (Ah) = P × cell capacity
- Energy (Wh) = pack voltage × pack capacity
- Maximum continuous current = P × cell current rating
- Maximum power = maximum current × pack voltage
Example: an e-bike pack
13S4P with 18650 lithium-ion cells of 3.6 V, 3 Ah, 10 A and 47 g:
- nominal voltage: 13 × 3.6 = 46.8 V (a “48 V” pack), 54.6 V fully charged and about 32.5 V empty;
- capacity: 4 × 3 = 12 Ah;
- energy: 46.8 × 12 ≈ 562 Wh;
- maximum continuous current: 40 A, or about 1,870 W;
- cell weight: 52 × 47 g ≈ 5.4 lb, before the case, BMS and wiring, which typically add 15 to 25%.
Cell chemistries
| Chemistry | Nominal | Full | Empty |
|---|---|---|---|
| Lithium-ion (NMC, NCA) | 3.6–3.7 V | 4.2 V | 2.5–3.0 V |
| LiFePO4 | 3.2 V | 3.65 V | 2.5 V |
| NiMH | 1.2 V | about 1.45 V | 1.0 V |
LiFePO4 has lower energy density but a longer cycle life and better thermal stability. Four LiFePO4 cells in series make a 12.8 V pack, a common replacement for 12 V lead-acid batteries.
Building a pack safely
- Use identical cells from the same batch, with matched capacity and internal resistance.
- Every lithium pack needs a battery management system (BMS) that monitors each series group, balances them and cuts off on overcharge, overdischarge, overcurrent and overtemperature.
- Spot-weld nickel strips; do not solder directly to cells.
- Size the wiring and fuse for the maximum current.
Air travel
Airlines allow lithium batteries up to 100 Wh in carry-on baggage, 100 to 160 Wh with approval, and generally refuse larger packs. Spare batteries must not go in checked luggage.