The low initial cost, ease of manufacture and relatively mature state of technology make lead-acid batteries the most popular energy storage choice for many applications. Lead-acid batteries exist in different configurations, each suitable for different applications and performance requirements. It is worth addressing the question as to whether model-based strategies can help realize even greater improvements in interrelated overall performance characteristics such as rate performance, cycle life and cost, and in overcoming factors that limit operational performance besides reducing product development time and cost by reducing the amount of testing required for development and validation. Some potential uses of model-based approaches are listed below:

1. For phenomena within lead-acid batteries for which no reliable or physically meaningful models exist, model development to provide a quantitative description may be useful. This may be a new physics-based model based on existing theory, a combination of existing models (e.g. extension to multiple spatial dimensions) or an empirical model with adjustable parameters which may be obtained by fitting experimental data. These mathematical models may then be used to simulate the time evolution of the relevant variables. Several continuum-level models with varying predictive capabilities have been reported in the literature^1-2. At the same time, there is scope for more complete descriptions of degradation phenomena such as irreversible sulfation, which is a major cause of cell failure.³
2. For situations where mathematical models exist, computationally efficient simulations may be performed by exploiting the mathematical structure of model equations to create suitable formulations.^4-5
3. Existing models may also be used to obtain useful qualitative and quantitative design insights. Parametric optimization of design parameters for a certain objective function is also possible, but is especially suitable with computationally efficient physics-based models.⁶ Different objective functions may be defined – total charge, local overpotentials etc. The optimization problem formulation can include mathematically equivalent constraints to prevent undesirable phenomena (e.g. sulfation, gas evolution). The use of physics-based models gives us predictions of state variables internal to the cell, which allows us to formulate a far more complete description of the problem than would be possible by simple empirical models.

Acknowledgements

The authors acknowledge financial support from the Department of Chemical Engineering and the Clean Energy Institute at the University of Washington.

References

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