Series, Parallel and Pack Design
From a 60V target to a bill of materials — S and P arithmetic, notation, a full worked e-rickshaw design, and the rules that prevent expensive mistakes.
Battery Fundamentals · Part 5 — Pack Design and Charging · Chapter 12 · 19 min read
Every pack is a decision about how to arrange the same energy. Series and parallel give identical watt-hours and completely different currents — and current is what determines your cable thickness, your losses, your heat and, in practice, your reliability. This chapter works one real pack from target to bill of materials.
20S1P
The Indian 60 V default
6.4 kWh
From 20 × 100 Ah LFP
~1C
Peak on a gradient
10 W
Per mΩ at 100 A
12.1 — The two connections
Series (S) — positive of one cell to negative of the next. Voltages add; capacity in amp-hours stays the same.
4 × (3.2 V / 100 Ah) in series = 12.8 V, 100 Ah = 1,280 Wh
Parallel (P) — all positives together, all negatives together. Capacities add; voltage stays the same.
4 × (3.2 V / 100 Ah) in parallel = 3.2 V, 400 Ah = 1,280 Wh
Important
The energy is identical. What differs is the current needed to deliver a given power — and since losses go as I²R, the series arrangement delivers the same power with far less heat and thinner cable. This is the entire reason electric vehicles moved from 48 V to 400 V to 800 V.
The electrical fundamentals are covered from first principles in Rocket Science, Chapter 6, if the arithmetic above went past too quickly.
12.2 — Reading 20S4P notation
20S4P means four cells in parallel forming a group, and twenty such groups in series. Eighty cells in total.
Technical framing
Order of assembly matters: parallel first, then series. Cells inside a p-group are directly connected, so they self-balance continuously and behave as one large cell. The BMS then monitors twenty voltages rather than eighty, which is why a 20S4P pack needs a 20-channel BMS and not an 80-channel one.
Configuration arithmetic
Pack voltage
V_pack = S × V_cell_nominal
Pack capacity
Ah_pack = P × Ah_cell
Pack energy
Wh_pack = S × P × V_cell × Ah_cell
Total cells
N = S × P
BMS channels
Channels = S
Not S × P — p-groups self-balance.
12.3 — Worked example — a 60 V e-rickshaw pack
Target: replace a 60 V / 100 Ah lead-acid bank of five 12 V blocks, deliver roughly 5 kWh usable, and work with the existing controller and a matched LFP charger.
12.3.1 — Step 1 — choose the series count
The bank being replaced swings between about 50 V empty and 73.5 V on charge. The LFP cell window is 2.5 to 3.65 V, so the question is which S count lands inside that envelope.
| Option | Nominal | Full charge | Cut-off | Verdict |
|---|---|---|---|---|
| 20S | 64.0 V | 73.0 V | 50.0 V | Excellent match to the lead-acid envelope. The mainstream choice in the Indian three-wheeler market. |
| 18S | 57.6 V | 65.7 V | 45.0 V | Lower top voltage — check the controller’s low-voltage cut-off does not trip early. |
Take 20S.
12.3.2 — Step 2 — choose cell and parallel count
Worked example 12.1 — Two ways to reach ~100 Ah at 20S
Using 100 Ah prismatic LFP cells, 20S1P:
Voltage: 20 × 3.2 = 64 V nominal
Capacity: 100 Ah
Energy: 64 × 100 = 6,400 Wh = 6.4 kWh
Usable at 90 % DOD: ~5.8 kWh
Using 32140 cylindrical LFP cells at 15 Ah each, 20S7P:
140 cells for 105 Ah — roughly 280 welds against 19
Same energy. The cylindrical route gives better failure containment and easier sourcing; the prismatic route gives a fifteenth of the joints, which on Indian roads is the stronger reliability argument. The trade is set out in Chapter 8.
12.3.3 — Step 3 — current and C-rate
- •Continuous draw of a loaded e-rickshaw: roughly 25 to 35 A, which on a 100 Ah pack is 0.25 to 0.35C. Comfortable.
- •Peak on a gradient: 90 to 110 A, around 1C. Verify this against the cell’s continuous discharge rating, not its peak rating — a hill is not a three-second pulse.
- •Charging at 15 A is 0.15C and about seven hours; at 30 A it is 0.3C and about three and a half hours. Both are gentle, and the slower one is better for life.
12.3.4 — Step 4 — size the BMS
- •20 channels.
- •Continuous current rating at least 1.5× expected continuous — 80 to 100 A.
- •Peak rating at least 150 to 200 A, with a stated duration.
- •Over-voltage cut at 3.65 V/cell, under-voltage cut at 2.5 V/cell, and a charge temperature lockout below 0°C.
Important
Size against continuous, never against peak. A BMS chosen on its peak figure runs its MOSFETs near their limit at ordinary load, and MOSFET arrays in cheap boards heat unevenly — one corner fails first and takes the pack with it.
12.3.5 — Step 5 — busbars and cable
At 100 A continuous, main cable is 16 to 25 mm². And the number worth committing to memory:
P = 100² × 0.001 = 10 W
Every millohm of connection resistance, at 100 A.
Ten watts per bad joint, inside a sealed enclosure, next to cells. Bad crimps are a leading cause of field failures, and they present as intermittent faults over bumps long before they present as heat.
12.3.6 — Step 6 — sanity-check the range
An e-rickshaw consumes roughly 45–70 Wh/km depending on load, terrain and driving
5.8 kWh usable ÷ 60 Wh/km ≈ 95 km
In plain English
Quote conservatively. Customers measure real range in their worst conditions — fully loaded, in traffic, uphill, in the heat — not in your best. A pack quoted at 95 km and delivering 70 km generates a warranty conversation; the same pack quoted at 70 km delivers a satisfied customer. The arithmetic is identical.
12.4 — Design rules worth internalising
- 1Never parallel packs that each have their own BMS unless the boards are explicitly designed for it. When one BMS cuts off, the entire load transfers instantly to the other, which then trips on over-current — or does not, and fails.
- 2Never parallel cells at different states of charge. The instantaneous equalisation current between cells 200 mV apart runs to hundreds of amps through a millohm of busbar, with nothing to limit it. Bring them within 50 mV first.
- 3Fuse the pack — a main fuse rated above peak load but below the cells’ short-circuit capability. On cylindrical designs, consider fusing at p-group level too, so one shorted cell cannot be fed by its parallel neighbours.
- 4Design for the worst cell, not the average. The pack’s capacity, its charge behaviour and its discharge behaviour are all set by the weakest series element — see Chapter 11.
- 5Every series connection is a potential failure point. Fewer, larger cells means fewer welds. That is a genuine reliability argument for prismatic cells in three-wheelers, and it is worth more than a marginal gain in energy density.
- 6Lay out for thermal gradient, not just peak temperature. Cells at the hot end of a 14°C spread age at several times the rate of the cool ones, and that becomes permanent capacity mismatch — see Chapter 6.
12.5 — Pack arithmetic cheat sheet
Everything you need for a first-pass pack design
Energy
Wh = Ah × V
Pack voltage
V_pack = S × V_cell
Pack capacity
Ah_pack = P × Ah_cell
Total cells
N = S × P
Current from C-rate
I = C-rate × Ah
C-rate from current
C-rate = I ÷ Ah
Charge time
t (h) = Ah ÷ I_charge × 1.1
The 1.1 covers the CV taper.
Voltage under load
V_load = OCV − (I × R_internal)
Heat generation
P_heat = I² × R
Series resistance
R_total = R1 + R2 + …
Cells in series.
Parallel resistance
R_total = R_cell ÷ P
Identical cells in parallel.
Usable energy
Wh_usable = Wh_pack × DOD limit × efficiency
Range
km = Wh_usable ÷ consumption (Wh/km)
Quick check: test yourself
1.Why is 20S the standard for a 60 V Indian three-wheeler rather than 18S?
Show answer
2.A customer wants more range and proposes wiring a second 60 V pack in parallel with the first. Both have their own BMS. What do you say?
Show answer
3.How many BMS channels does a 20S4P pack need, and why not 80?
Show answer
4.Your pack draws 100 A continuous and one busbar joint measures 1.5 mΩ. Is that a problem?
Show answer
Chapter summary
- ✓Series adds voltage, parallel adds capacity, and the energy is identical. What differs is current — and since losses go as I²R, higher voltage means less heat and thinner cable.
- ✓20S4P means four in parallel, twenty groups in series, eighty cells — and twenty BMS channels, because p-groups self-balance and behave as one cell.
- ✓Assemble parallel first, then series. It is not a convention; it is what makes the channel count work.
- ✓20S LFP at 64 V nominal, 73 V full and 50 V cut-off matches the 60 V lead-acid envelope, which is why it is the Indian three-wheeler default.
- ✓A 20S1P pack of 100 Ah LFP cells is 6.4 kWh, about 5.8 kWh usable at 90 % DOD, and roughly 95 km at 60 Wh/km — quote conservatively against that.
- ✓Size the BMS on continuous current at 1.5× expected load, never on its peak figure.
- ✓Every millohm of connection resistance dissipates 10 W at 100 A. Bad crimps are a leading field failure and they present as intermittent faults first.
- ✓Never parallel independently-managed packs, never parallel cells more than 50 mV apart, fuse the pack, and design for the worst cell and the thermal gradient rather than the averages.
Frequently asked questions
What does 20S4P mean?+
Four cells in parallel forming a group, and twenty such groups in series — eighty cells in total. Order matters: parallel first, then series. Cells inside a parallel group are directly connected, so they self-balance continuously and behave as one large cell, which is why a 20S4P pack needs a 20-channel BMS rather than an 80-channel one.
Why is 20S standard for a 60V Indian three-wheeler?+
Because it matches the envelope of the lead-acid bank it replaces. 20S LFP gives 64.0V nominal, 73.0V fully charged and 50.0V at cut-off, which sits almost exactly where a 60V lead-acid bank swings — so the existing controller and its low-voltage cut-off behave as before. 18S gives 57.6V nominal and risks the controller cutting out early.
How do I size the BMS for a pack?+
Channels equal the series count. Continuous current rating should be at least 1.5 times expected continuous draw — 80 to 100A for a pack drawing 25 to 35A with 1C peaks. Peak rating at least 150 to 200A with a stated duration. Then set over-voltage at 3.65V per cell, under-voltage at 2.5V, and a charge temperature lockout below 0°C. Size against continuous, never against peak.
Can I connect two battery packs in parallel?+
Not if each has its own BMS, unless the boards are explicitly designed for it. When one BMS trips — on temperature, a low cell, anything — the entire load transfers instantly to the other pack, which then sees roughly double the current it was sized for. The packs also age differently and will fight each other. Use a single larger pack, or boards with an explicit parallel mode and a shared control line.
How much energy does a 20S1P pack of 100Ah LFP cells hold?+
6.4 kWh nominal — 20 × 3.2V × 100Ah — of which roughly 5.8 kWh is usable at 90 per cent depth of discharge. At a typical e-rickshaw consumption of 60 Wh/km that is about 95 km, though you should quote conservatively: customers measure real range fully loaded, in traffic, uphill and in the heat.
How much does a bad electrical joint cost in a pack?+
Ten watts per millohm at 100A, from P = I²R. That is a soldering-iron tip inside a sealed enclosure next to cells, and it gets worse rather than settling because resistance rises with temperature. Busbar joints should measure under about 50 µΩ. Bad crimps are a leading cause of field failures and present as intermittent faults over bumps before they present as heat.
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Battery Fundamentals is an original educational series on lithium battery technology. Threshold tables, cycle-life curves and worked examples use representative values drawn from published product specifications and widely-observed industry patterns, not measured data from a specific product. Always consult the current manufacturer datasheet before making design, purchasing, warranty or certification decisions.