Lead-Acid Models

Physics-based lead-acid battery models in PyBaMM, including the Full porous-electrode model, the Leading-Order Quasi-Static (LOQS) model, and BasicFull.

PyBaMM includes a set of physics-based models for lead-acid batteries derived from the Newman-Tiedemann porous-electrode framework. All models are available under the pybamm.lead_acid namespace.

Lead-acid models use pybamm.LeadAcidParameters and default to the Sulzer2019 parameter set. Unlike lithium-ion models, there are no particles: the electrode active material is modelled as a solid reactant with no diffusion.

Available models

Model	Electrolyte diffusion	Spatial resolution	Use case
Full	Full (spatially resolved)	Full 1D	High-fidelity simulation
LOQS	Leading-order (spatially averaged)	0D / 1D	Fast simulation, parameter sweeps
BasicFull	Full	Full 1D	Education and model exploration

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Models

Full

Full model

The Full model is a porous-electrode model for lead-acid batteries based on the Newman-Tiedemann framework as described in Sulzer et al. (2019). It resolves spatial distributions of electrolyte concentration and potential, electrode potential, and porosity across the cell sandwich.

When to use: High-accuracy simulations where spatial gradients in electrolyte concentration and porosity are important, including during high-rate discharge or charge.

Reference: Sulzer, V., et al. (2019). Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part I. Physical Model. Journal of The Electrochemical Society.

import pybamm

model = pybamm.lead_acid.Full()
print(model.name)  # 'Full model'

param = model.default_parameter_values  # Sulzer2019
sim = pybamm.Simulation(model, parameter_values=param)
sim.solve([0, 3600])
sim.plot()

LOQS

Leading-Order Quasi-Static model

The LOQS model is derived by an asymptotic expansion in the applied current, retaining only the leading-order terms. Electrolyte concentration and porosity are spatially uniform (x-averaged). This makes the model significantly faster than the Full model.

When to use: Rapid simulations, state estimation, parameter identification, or any case where spatial gradients in the electrolyte are secondary.

Reference: Sulzer, V., et al. (2019). Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part II. Asymptotic Analysis. Journal of The Electrochemical Society.

The LOQS model does not use a Jacobian by default when dimensionality=0. This makes it particularly efficient for 0D simulations.

import pybamm

model = pybamm.lead_acid.LOQS()
print(model.name)  # 'LOQS model'

sim = pybamm.Simulation(model)
sim.solve([0, 3600])
sim.plot()

BasicFull

BasicFull

The BasicFull model implements the same physics as Full but in a single self-contained class, making the governing equations directly visible. It does not use the submodel architecture and is less flexible, but is easier to read and modify for educational purposes.

When to use: Understanding the governing equations, developing new models, or teaching. For production use, prefer pybamm.lead_acid.Full.

Reference: Sulzer, V., et al. (2019). Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part I. Physical Model. Journal of The Electrochemical Society.

import pybamm

model = pybamm.lead_acid.BasicFull()
print(model.name)  # 'Basic full model'

sim = pybamm.Simulation(model)
sim.solve([0, 3600])
sim.plot()

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Lead-acid specific options

Hydrolysis (oxygen evolution)

Lead-acid cells produce oxygen at the positive plate during overcharge via electrolyte hydrolysis. Enabling this option adds oxygen diffusion and reaction submodels.

Option	Values	Default
"hydrolysis"	"false", "true"	"false"

When "hydrolysis" is "true", "surface form" cannot be "false". Use "algebraic" or "differential" instead.

model = pybamm.lead_acid.Full(
    options={
        "hydrolysis": "true",
        "surface form": "algebraic",
    }
)

Convection

Gas evolution during charge drives electrolyte convection. This can be modelled with a uniform transverse or fully resolved transverse convection model.

Option	Values	Default
"convection"	"none", "uniform transverse", "full transverse"	"none"

model = pybamm.lead_acid.Full(
    options={"convection": "uniform transverse"}
)

Thermal

Option	Values	Default
"thermal"	"isothermal", "lumped", "x-lumped", "x-full"	"isothermal"

model = pybamm.lead_acid.Full(
    options={"thermal": "lumped"}
)

Operating mode

Control how the external circuit condition is applied. The LOQS model supports callable operating modes via an algebraic constraint.

Option	Values	Default
"operating mode"	"current", "voltage", "power", "resistance", "CCCV", callable	"current"

model = pybamm.lead_acid.LOQS(
    options={"operating mode": "voltage"}
)

Example with options

import pybamm

# Full lead-acid model with oxygen evolution and uniform convection
model = pybamm.lead_acid.Full(
    options={
        "hydrolysis": "true",
        "surface form": "algebraic",
        "convection": "uniform transverse",
        "thermal": "isothermal",
    }
)

param = model.default_parameter_values  # Sulzer2019
sim = pybamm.Simulation(model, parameter_values=param)
sim.solve([0, 3600])
sim.plot()

Call pybamm.print_citations() after running a simulation to get the full citation list for the models and parameters used.