Battery knowledge · Transport and modelling
Single-particle model
A simplified physics model that represents each electrode as one spherical particle and neglects electrolyte gradients. It runs fast enough for a BMS and is accurate at low to moderate currents.
- Abbreviation
- SPM
Example
Transport and modelling: an example situation
The same concentration difference across 10 μm gives ten times the gradient across 100 μm; at equal D, first-law flux magnitude is ten times greater.
Read Single-particle model alongside Battery management system in this context. The electronics and software that keep a battery inside its safe window: measuring every cell voltage and many temperatures, estimating SOC and SOH, balancing cells, computing current limits, controlling the contactors and reporting over the vehicle network.
Use in Lemonergy
Lemonergy Studio blocks
Single-particle cell worked example
Native spherical solid diffusion and Butler-Volmer kinetics with tabulated electrode OCPs. Isothermal material parameters; no electrolyte transport, aging or conserving adapter.
Blocks to use
- Single-particle cell
Solves spherical solid diffusion in separate negative and positive representative particles with conservative radial finite volumes. Opposite Faradaic fluxes transfer lithium between electrodes. Surface stoichiometries drive tabulated OCPs and Butler-Volmer overpotentials; temperature is prescribed.
Inputs & settings
- Use the parameter values in the block reference.
- Bundled example verified on the production release of 28 October 2026.
This overview identifies the components to use. Follow the example in Lemonergy for their connections and settings.
- Review the block inputs, units and model limits.
- Open the Studio example and run its bundled model.
- Compare the output channels with the numerical checks; change one input and run again.
Example. Use the defaults below with Signed cell current = 1 A, Kinetics temperature = 298.15 K. At 0 s, Terminal voltage is 3.912048435 V. Additional checks are listed below.
Observe. Inspect the outputs and numerical checks on the block reference page.
Fixed solid diffusion and material coefficients; no electrolyte transport, aging, thermal state or conserving boundary adapter. Surface concentrations must stay strictly inside their physical range. The cited paper explains model assumptions and a richer electrolyte extension; this block implements the stated solid-only model. The example verifies numerical behavior for synthetic parameters. Cell characterization and validation for an intended use are separate tasks.
Open Studio example →References & further reading
Further reading on this topic
These sources provide broader context; they are not presented as citations for every statement in this entry.
- Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell
Marc Doyle, Thomas F. Fuller, John Newman · Journal of The Electrochemical Society · 1993
Topic background · Porous-electrode transport and insertion-cell modeling; foundational work rather than a specification for a particular commercial cell.
- Quantities, Units and Symbols in Physical Chemistry, 3rd edition, 2nd printing
IUPAC · 2011
Topic background · Physical-chemistry notation, thermodynamics, electrochemistry and transport quantities.