Cell Arrangement, Voltage, Capacity
& Energy Calculations
The mathematical backbone of every battery pack — from the rules of series and parallel connections to fully worked EV and ESS pack sizing examples. Master this and you can design any battery configuration from scratch.
A single lithium-ion cell is a limited device. A typical cylindrical 21700 cell delivers approximately 3.6 V and 5 Ah — enough to power a small LED for a few hours, but wholly insufficient for an electric vehicle, an energy storage system, or even a high-performance power tool. To build battery systems that meet real-world requirements, cells must be connected together in deliberate configurations.
Cell arrangement is the architectural foundation of every battery pack. It determines the pack's voltage, current capability, total energy, and to a significant extent, its safety behaviour, thermal characteristics, and long-term degradation profile.
Understanding cell arrangement is not purely mathematical — it has direct implications for safety, thermal management, and BMS design. Mismatched cells in a series string accelerate imbalance. Poor parallel group design can create dangerous internal circulation currents. Every decision in cell arrangement has consequences that ripple through the entire pack design.
When cells are connected in series, the positive terminal of one cell is connected to the negative terminal of the next. Voltages of all cells add together while capacity remains equal to that of a single cell.
The voltage drop due to internal resistance in a series string is cumulative. Each cell contributes its own I×R drop:
Designing electronics to the nominal pack voltage only and ignoring the full voltage swing from V_min to V_max. Every component connected to the pack — inverters, converters, chargers, motor controllers — must be rated for the maximum voltage the pack can ever produce: n × V_cell_max.
When cells are connected in parallel, all positive terminals are connected together and all negative terminals are connected together. Voltage remains equal to that of a single cell while capacity and current capability multiply.
If cells in a parallel group have different states of charge when first connected, significant equalisation currents will flow between them. These can be very large if the SOC difference is significant — potentially damaging cells. Parallel cells must always be pre-charged to approximately the same SOC (within ±20 mV OCV) before connection.
Real-world battery packs almost always use a combination of series and parallel connections — denoted as nS×mP — where n is the number of cells in series and m is the number of cells in parallel. This notation allows the designer to independently target voltage and capacity requirements.
Parallel groups first (P→S): Build m-cell parallel groups, then connect groups in series. Within each group, cells are continuously equalised — this is the most common and recommended approach in module design. Series strings first (S→P): Build full series strings, then connect strings in parallel — harder to pre-balance and can create inter-string imbalance over time.
Pack voltage calculation is one of the most fundamental skills in battery pack design. The designer must always calculate three distinct pack voltage values — nominal, maximum, and minimum — for any series configuration.
| Series Count | Chemistry | Nominal | Maximum | Minimum | Application |
|---|---|---|---|---|---|
| 4S | NMC | 14.4 V | 16.8 V | 11.2 V | 12V Systems |
| 4S | LFP | 12.8 V | 14.6 V | 10.0 V | 12V LFP |
| 13S | NMC | 46.8 V | 54.6 V | 36.4 V | 48V Systems |
| 16S | LFP | 51.2 V | 58.4 V | 40.0 V | 48V LFP |
| 96S | NMC | 345.6 V | 403.2 V | 268.8 V | 400V EV |
| 104S | LFP | 332.8 V | 379.6 V | 260.0 V | 400V EV (LFP) |
| 108S | NMC | 388.8 V | 453.6 V | 302.4 V | 400V Premium |
Pack capacity — the total charge the pack can store and deliver in ampere-hours — is determined entirely by the number of cells in parallel. Series connections do not add capacity; they only add voltage.
A 200 Ah pack at 12V = 2.4 kWh. A 200 Ah pack at 400V = 80 kWh. Same capacity — completely different energy and application. Always quote pack voltage alongside capacity. Quoting Ah alone without voltage is meaningless for energy comparison across different systems.
Pack energy — measured in watt-hours (Wh) or kilowatt-hours (kWh) — is the most practically important metric for characterising a battery system's real-world usefulness. The total pack energy is simply the number of cells multiplied by the energy of a single cell.
For EV range calculations, it is the usable energy — not nominal energy — that determines how far the vehicle can travel. A 6.91 kWh nominal pack with an 80% usable window delivers only 5.53 kWh usable. Pack designers must always be explicit about which figure they are quoting.
Four fully worked examples covering the complete range from small auxiliary systems to large EV traction packs. Each follows the same structured design process: target → series count → parallel count → full verification.
Cell matching is the practice of selecting cells for a pack that have closely similar specifications — particularly capacity, internal resistance, and self-discharge rate — to minimise the imbalance that develops in series strings over time.
High-volume manufacturers use automated cell graders — systems that measure capacity, internal resistance, and OCV for every cell and sort them into matched bins. In the EV industry, A-grade cells meet the full specification, B-grade cells fall within a wider tolerance, and C-grade cells are used in less demanding applications. Pack designers specify required grade in procurement specifications.
Cell imbalance — differences in SOC, capacity, or internal resistance between cells — is one of the most practically important phenomena in battery pack engineering. Understanding how imbalance develops, how it manifests, and how it affects pack performance and longevity is essential for any designer.
In a parallel group, cells are continuously equalised by the parallel connection — any voltage difference causes an equalisation current to flow immediately. This means parallel groups are inherently self-balancing and do not require active balancing within the group.
However, imbalance in parallel groups manifests as unequal current sharing. The cell with the lowest internal resistance carries more current than its neighbours. Over thousands of cycles, this means the lowest-resistance cell cycles more intensively than others in the group, degrading faster — gradually increasing its resistance and slightly re-distributing the load. Parallel groups should therefore be built from cells with closely matched internal resistance.
Temperature non-uniformity within a pack is one of the most dangerous and long-lasting sources of imbalance. Cells at higher temperatures have lower internal resistance and different degradation kinetics — in a pack where the thermal management creates a temperature gradient, cells at different positions will degrade at different rates over time, creating a systematic spatial pattern of imbalance that compounds with every cycle. Uniform temperature distribution is therefore a primary objective of thermal management design — not just for immediate performance, but for long-term pack health.
The best imbalance management strategy is prevention, not correction. Use matched cells, design for uniform temperature distribution, limit maximum DOD, and size balancing circuits correctly from the start. Rely on balancing circuitry to compensate for unavoidable drift — not to compensate for poor cell selection or poor thermal design.
