A cell-level model – an Equivalent Circuit Model, a Single Particle Model, or a full Doyle Fuller Newman Battery Model – only gets you so far once it has to represent a full pack. Packs introduce problems that don’t exist at single-cell scale: no two cells behave identically, heat generated in one cell affects its neighbours, and the electrical interconnects (busbars, welds, contactors) add their own resistance and thermal mass. This page groups the general families of technique used to model that pack-level behaviour, alongside worked examples already on the site.
- Series/parallel scaling with cell-to-cell variation: the simplest extension of a validated cell model – replicate it across the pack’s series/parallel topology – only becomes realistic once each replica is given its own sampled parameters (capacity, resistance, impedance) rather than assuming every cell is identical. This is what lets a model capture how manufacturing tolerance and local thermal gradients cause individual cells to diverge from the pack average over life. See Digital Twin of a Battery Module for a worked example of predicting per-cell state from busbar and weld quality.
- Lumped-parameter electro-thermal networks: pairing an electrical ECM with a thermal resistor-capacitor network representing heat flow between cells, busbars, cooling plate and enclosure. These stay simple enough to run in real time on a BMS or across many design scenarios, at the cost of spatial detail within each cell. See Cell Busbar Thermal Model for a simple worked example of this approach applied to a single interconnect.
- Reduced-order/surrogate models: distilling a high-fidelity electrochemical or 3D thermal model down to a fast approximation suitable for embedded or real-time use, trading some accuracy for speed. See Control-Oriented Reduced-Order Models, which benchmarks reduced-order and enhanced single-particle models against a full-order simulation.
- High-fidelity 3D thermal/CFD models: full three-dimensional simulation of pack cooling, used at the design stage to evaluate cooling plate geometry, coolant flow direction and module layout before hardware exists. Too slow for real-time use, but valuable for one-off design studies. See Tesla Fast Charge Thermal Model, What is the Optimum Design of a Cooling Plate for Uniform Cooling?, and Performance Analysis of an Integrated BEV Thermal Management.
- Digital twins: a live, continuously updated pack model – typically a reduced-order physics model kept in sync with real-time sensor and BMS data – used to track the state of health of the actual physical pack in the field and forecast its remaining life, rather than to explore design options offline. See the Digital Twin page.
- Sizing/system-boundary models: simple, often spreadsheet-based models used early in design to size a pack against a duty cycle before any detailed cell or thermal model exists. See the Battery Calculations Workbook‘s Pack Sizing sheet, BESS Sizing, and the Electric Vehicle Range Calculator.
References
- Zhu, T., Thermally Aware Design of Large-Format Batteries Driven by an Equivalent Circuit Network-Based Electro-Thermal Model, Batteries, Vol. 12, Issue 2, 2026
See also: Equivalent Circuit Model, Digital Twin, Thermal Runaway Modelling at Cell Level, Cell to Cell Variation, Heat Generation in a Cell, Thevenin Model