Battery knowledge · Transport and modelling
Equivalent circuit model
A cell model built from a voltage source for OCV, a series resistor and one or more RC pairs for the slower dynamics. Its few parameters are fitted from pulse tests, and it is what most battery management systems run in real time. [1]
- Abbreviation
- ECM
- Also called
- Thevenin model
Example
Voltage response and relaxation
At τ = 20 s, 63.2% of the step response is complete; a relaxation retains 36.8%.
Two separate analytical experiments; normalized voltage, not measured data.
Explore the graph
One time constant completes about 63% of a first-order voltage change.
At τ = 20 s, 63.2% of the step response is complete; a relaxation retains 36.8%.
τ = RC; step response = 1 − e^(−t/τ)
Illustrative model. Two separate analytical experiments; normalized voltage, not measured data.
Use in Lemonergy
Lemonergy Studio blocks
Electrothermal ECM cell worked example
Causal current-to-voltage model with charge and thermal states. Conserving ports are not yet included.
Blocks to use
- Electrothermal ECM cell
Accepts signed discharge current, ambient temperature and external heat. Charge balance drives SOC; an OCV table sets equilibrium voltage. The ECM adds two RC polarization states. Both variants include an ohmic loss and a lumped temperature state.
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 (discharge positive) = 2 A, Ambient temperature = 298.15 K, External heat flow = 0 W. At 0 s, Terminal voltage is 3.68 V. Additional checks are listed below.
Observe. Inspect the outputs and numerical checks on the block reference page.
The external interface is causal current-to-voltage, without conserving terminals. Parameters are constant except the one-dimensional SOC-to-OCV table. No hysteresis, aging, reversible entropic heat or automatic parameter identification. The example verifies numerical behavior for synthetic parameters. Cell characterization and validation for an intended use are separate tasks.
Open Studio example →Lemonergy Studio blocks
State-space impedance worked example
Continuous current-to-voltage linear dynamics with direct feedthrough. User supplies identified matrices.
Blocks to use
- State-space impedance
Solves a user-supplied continuous linear state model from current inputs to voltage outputs. Dense matrices support multiple input/output channels and direct feedthrough. Matrices are displayed as rows in configuration.
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 Current inputs = [2] A. At 0 s, Voltage outputs is [0.02] V. Additional checks are listed below.
Observe. Inspect the outputs and numerical checks on the block reference page.
At most 16 states and eight inputs or outputs. The model author must identify stable, physically meaningful matrices and consistent units. No automatic impedance fitting is performed. The example verifies numerical behavior for synthetic parameters. Cell characterization and validation for an intended use are separate tasks.
Open Studio example →Lemonergy Studio blocks
Tabulated OCV cell worked example
Causal current-to-voltage model with charge and thermal states. Conserving ports are not yet included.
Blocks to use
- Tabulated OCV cell
Accepts signed discharge current, ambient temperature and external heat. Charge balance drives SOC; an OCV table sets equilibrium voltage. The ECM adds two RC polarization states. Both variants include an ohmic loss and a lumped temperature state.
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 (discharge positive) = 2 A, Ambient temperature = 298.15 K, External heat flow = 0 W. At 0 s, Terminal voltage is 3.68 V. Additional checks are listed below.
Observe. Inspect the outputs and numerical checks on the block reference page.
The external interface is causal current-to-voltage, without conserving terminals. Parameters are constant except the one-dimensional SOC-to-OCV table. No hysteresis, aging, reversible entropic heat or automatic parameter identification. The example verifies numerical behavior for synthetic parameters. Cell characterization and validation for an intended use are separate tasks.
Open Studio example →All connected Lemonergy block references
References & further reading
Technical references
- Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2. Modeling and identification
Gregory L. Plett · Journal of Power Sources · 2004
Technical reference · Battery charge balance, open-circuit voltage, ohmic loss, polarization dynamics and model identification; parameters require cell-specific data.
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.