How Engineers Size Battery & EV Systems

How engineers size battery and EV systems

Battery pack design is a multi-physics problem — electrical, thermal, and safety requirements all interact. Engineers must size the series-parallel cell configuration for voltage and energy, estimate ohmic heating to size the cooling system, check busbar current density, and provide vent area for abuse-scenario gas release. These screening calculations happen at the concept stage, well before detailed electrochemical or CFD modelling.

This guide covers pack topology, thermal management, busbar sizing, and safety vent screening for lithium-ion packs.

Pack configurations and applications

Engineering workflow

1. Define voltage and energy target — from drivetrain or application requirements.
2. Select cell — chemistry, format (cylindrical, prismatic, pouch), voltage, capacity, resistance.
3. Configure topology — $N_s$ series for voltage, $N_p$ parallel for capacity/current sharing.
4. Compute pack energy — $E=V_{\mathrm{pack}}\times N_p\times C_{\mathrm{Ah}}$.
5. Estimate heating — $P=N_{\mathrm{total}}\times I_{\mathrm{cell}}^2\times R_{\mathrm{cell}}$ at peak current.
6. Size cooling — flow rate for allowable coolant temperature rise.
7. Size busbars — cross-section from pack current and allowable current density.
8. Screen vent area — for worst-case gas generation during thermal runaway.

Key quantities and formulas

Pack voltage and energy:

Ohmic heat generation:

Cooling mass flow:

Busbar minimum cross-section:

Worked example

Given: Passenger EV — 96s4p NMC cells, each 3.7 V nominal, 60 Ah, internal resistance 1.5 m$\Omega$. Peak discharge current 200 A (pack). Coolant: 50/50 glycol-water ($c_p=3400$ J/kg·K), $\Delta T_{\mathrm{allow}}=8$ K. Busbar current density limit 5 A/mm².

1. Pack voltage: $96\times 3.7=355$ V. Energy: $355\times 4\times 60/1000=85.2$ kWh.
2. Cell current at peak: $200/4=50$ A per cell.
3. Heat generation: $96\times 4\times 50^2\times 0.0015=1,440$ W.
4. Cooling flow: $\dot{m}=1,440/(3,400\times 8)=0.053$ kg/s ($\approx 3.0$ L/min).
5. Busbar area: $200/5=40$ mm² — equivalent to a 7.1 mm diameter round bar or 10 × 4 mm flat bar.

Interpretation: The 1.4 kW heat load is manageable with a modest coolant loop. At sustained fast-charge rates (e.g., 2C), heat doubles — re-evaluate cooling and cell temperature limits.

Common mistakes and checks

• Using nominal voltage for energy but minimum voltage for power calculations — be consistent with the use case.
• Ignoring cell-to-cell resistance variation — worst-case cell sees highest current in parallel strings.
• Sizing cooling for average load when peak or fast-charge load governs.
• Using copper current density rules for aluminium busbars without adjusting for lower conductivity.
• Treating the vent area calculation as regulatory compliance — it is a first-pass screen only.
• Forgetting entropic heat — reversible heat from electrochemistry adds to $I^{2}R$ at high C-rates.

FAQ

How do I choose between series and parallel cell count?

Series count sets pack voltage; parallel count sets capacity and current sharing. Increase $N_s$ for higher voltage (motor efficiency). Increase $N_p$ for more energy or to reduce per-cell current.

What internal resistance should I use?

Use the manufacturer's DC internal resistance (DCIR) at the expected temperature and SOC. DCIR increases at low temperature and low SOC. For screening, use the room-temperature mid-SOC value.

How is vent area estimated?

The module uses a volumetric gas flow from an assumed gas generation rate during thermal runaway, divided by a target vent velocity, to give a minimum vent opening area. This is a screening estimate — certified vent design requires testing per UL 2580 or IEC 62619.

What about cell balancing and BMS?

This module sizes the pack electrically and thermally. Cell balancing (passive or active) and battery management system (BMS) logic are control/electronics design topics not covered here.

How does temperature affect pack performance?

Cold reduces capacity and increases resistance (higher heating). Hot accelerates degradation. Most Li-ion cells operate best between 15–35 °C. Size the cooling system to keep cell temperature in this window.

Use the PhyCalcPro calculator

Open the Battery & EV systems calculator. Enter cell specs, pack topology, current, cooling parameters, and busbar limits. Review pack energy, heat generation, required cooling flow, busbar area, and vent screening area.

Purpose

Screen battery pack nominal energy, ohmic heat generation, required cooling flow, minimum busbar cross-section, and simple vent area for EV and stationary storage packs at concept design stage.

Physics & theory

Pack configuration: $N_s$ series times $N_p$ parallel cells. Nominal voltage $V_{\mathrm{pack}}=N_s{V}_{\mathrm{cell}}$; energy $E=V_{\mathrm{pack}}{N}_p{C}_{\mathrm{Ah}}$. Cell heating from internal resistance: $P=N_{\mathrm{total}}{I}_{\mathrm{cell}}^2{R}_{\mathrm{cell}}$. Coolant flow $\dot{m}=P/(c_p\Delta T)$. Busbar area from current density limit. Vent area from gas flow and target velocity — first-pass screen only.

Governing equations

Numerical method

Closed-form pack electrical and thermal screening. Vent area from gas generation rate divided by target velocity — not full thermal runaway simulation.

Inputs

Outputs

• Pack voltage, energy (kWh), heat generation (W), cooling mass flow, busbar area (mm²), vent area (m²).

Design codes & checks

• Indicative: Pack energy, heat, vent screening
• ISO: ISO 6469 electric road vehicle safety (context)
• UL: UL 2580 battery safety (context)
• SAE: SAE J2464 abuse testing (context)

Assumptions & limitations

• Uniform cell parameters; no cell-to-cell imbalance or BMS logic.
• $I^{2}R$ heating only; no entropic heat or reaction heat during abuse.
• Vent sizing is volumetric screen — not regulatory compliance tool.
• No propagation, enclosure rupture, or state-of-charge maps.

References

1. Plett, G. L. Battery Management Systems, Vol. I & II. Artech House.
2. ISO 6469-1:2019. Electrically propelled road vehicles — Safety specifications.
3. UL 2580. Batteries for Use in Electric Vehicles.
4. SAE J2464. Electric and Hybrid Electric Vehicle Rechargeable Energy Storage System Safety.