About:SPMe
Single Particle Model (with Electrolyte) - Enhanced electrochemical modeling with electrolyte transport for improved accuracy
Overview
About:SPMe is a physics-based model that represents the battery according to a set of physical equations and a corresponding parameter set. It is an implementation of a Single Particle Model with Electrolyte (SPMe). This is a streamlined simplification of the Doyle-Fuller-Newman model used in About:DFN.
About:SPMe predicts:
- Current-voltage relation
- Battery heat dissipation rate
- Individual electrode overpotentials
- Lithiation distribution within active material particles (electrode-averaged)
- Electrolyte distribution across electrodes and separator
About:SPMe accounts for:
- State-of-charge (SOC)
- Temperature
- Charge-discharge hysteresis
- Rate capability (according to physics-based loss computation)
- Cycling history
Technical Description
About:SPMe implements a 1D model in which the macroscopic current-flow direction in each electrode pair is resolved as a linear 1D domain. Macroscopic properties are coupled to a representation of the microscopic active material particle properties assuming a single representative spherical particle of a Li insertion material in each electrode. All particles of a given material are assumed to have constant size and equivalent behaviour; particle size and shape distributions are not considered, and heterogeneity of electrochemical response of particles at different electrode locations is ignored.
The macroscopic 1D DFN model predicts the electrolyte current density and the flux of Li\(^+\)-containing electrolyte by solving concentrated solution transport equations for the electrolyte concentration and electrolyte potential. In electron-conducting regions, current density is predicted using Ohm’s law, solving for electric potential. Morphology of porous structures (electrodes and separator) is described using a porous transport theory in terms of homogenised properties (porosity, tortuosity).
Li insertion rate and the corresponding faradaic current density is coupled in an electrode-averaged manner according to a specified volumetric surface area to a microscopic 1D model, which solves the spherically symmetric Fick’s law diffusion equation to predict inserted Li concentration as a function of particle radius.
Internal heating is computed, including Joule heating (resistive loss) and activation overpotential. Heat of mixing is ignored, to the first approximation. Temperature dependence of various physical quantities is accounted for by the specification of Arrhenius activation energies.
Key features
- Faster solution time than About:DFN, at the expense of reduced physical detail
- Compatible with any thermal model
- Compatible with distributed electronic networks and 3D cell/module/pack models
- Implements a subset of About:DFN, in which, for each electrode, all active material particles are considered equivalent. This is called the single-particle model with electrolyte (SPMe).
Key applications
- System prototyping for cell integration
- Fast charge protocol design
- Representation of cell performance in 3D thermal models
- Degradation analysis*
* with provision of supplementary degradation data