Automatic Parametrisation Procedure for Equivalent Circuit Models of Li-Ion Batteries

Abstract

In recent years, electrification of automotive powertrains has been increasingly considered and
implemented as a key element in attaining new affordable, more efficient, and potentially sustainable forms
of transportation. Since they represent a defining element of any electrified vehicle, energy storage systems
are receiving an increasing amount of attention from the research community as well as the automotive
industry. This is most often aimed towards Li-ion batteries and pursues to improve their performance and
lifespan while reducing cost and environmental impact through advancements in the development and
manufacturing of the system as well as its operation and recycling.

One of the most effective tools in supporting all lifecycle stages of a battery system is represented by
simulation models, ranging from static data-driven representations to complex multidimensional virtual
depictions of electrochemical cells. Due to the trade-off between the resources required to develop and the
ability to replicate the voltage response as well as the vast array of applications, the equivalent circuit model
is one of the most popular options employed for simulating battery systems. While the usefulness of any
model is always determined by its structure, accurate and effective parametrisation of the structure in relation
to the system to be replicated also represents a highly important prerequisite for all applications.

The aim of this thesis is to discuss the development and evaluation of a novel parametrisation
methodology suitable for equivalent circuit models and exemplified for the Li-ion battery use case. The
research presented fills a substantial research gap for accurate and effective procedures capable of
parametrising the specified model in an automated manner. These attributes reliably allow the use of
unconstrained time-domain datasets capturing the voltage response of the system and further strengthen the
ability to complement the dataset by using prior models as alternative sources of information.

The development and evaluation of the proposed methodology were supported by a readily available
equivalent circuit model supplied by the industrial sponsor. The first part of the research focuses on the
assembly of the procedure, which creates an estimate of the model and iteratively improves it by refining the
values of its parameters through a series of steps. The second part evaluates the resulting methodology using
a wide array of cases defined by the time-domain data and the prior model used for training. The two main
aspects investigated are the ability of the parametrisation procedure to efficiently convert time-domain
information into an accurate model as well as its ability to reduce the requirement for data by using
information supplied by the prior model.

The accuracy and computational efficiency demonstrated endorse the proposed methodology as a
state-of-the-art solution. The process was highly consistent in achieving model MSE values below 1E−3 V²
across large individual data files used for training as well as validation but also presented values as low as
2.83E−5 V². To obtain an accurate evaluation of the computational efficiency, a partially streamlined version
of the proposed methodology was implemented. Despite the non-optimised code, the parametrisation of 409
individual model parameter values distributed across 6 lookup tables using 24.543 hours of data was
completed in 999.1 seconds. A comparison study published by Savu et al.[1] in a separate article targeting
smaller scale versions suitable for small segments of data demonstrates that the proposed parametrisation
principle requires 75 times less computational effort than a readily available global solver, while the expansion
to the complete model is also likely to increase this factor exponentially. Further work aimed at computational
time optimisation also suggests a margin of improvement, potentially by an order of magnitude, that could be
achievable through optimisation of the code and parallelisation techniques.

Outside accuracy and computational efficiency, the results also support the ability of the proposed
parametrisation methodologies to include prior information towards improving interpolation and
extrapolation capabilities of the model outside its trained regions as well as reducing the amount of data
required and, implicitly, testing efforts. To exemplify, a model representative of a Samsung 30Q cell was used
as prior information for the parametrisation of a model set to replicate a similar Sony VTC6 cell. An accuracy
improvement of over 80% that of a model parametrised using the complete training dataset was achievable
by using as low as only 31% of the data in the presence of the informed prior. The consistency of the result
was also confirmed by reverted cases employing the model parametrised for the Sony VTC6 as the prior
information for models replicating the Samsung 30Q cell. Key factors determining the effectiveness of the
technique include the level of similarity between the system producing the prior and the system to be
modelled, as well as the distribution of the data relative to operating conditions.

The outcome of the research presents a significant positive impact on multiple elements associated
with simulation models. The methodology provides a gateway to efficiently obtaining models in an automated
manner with limited time, effort and resources required, hence supporting their adoption in research and
development activities as well as frontloading these activities in virtual environments. The process also
represents a showcase of compiling unconstrained (‘as found’) datasets into accurate models, reducing the
requirements imposed on training data and becoming directly suited to effectively using data lakes. The ability
to include prior models as alternative sources of information will enhance the model obtained while employing
only an unconstrained dataset and will also reduce the amount of data required and, implicitly, testing efforts.
Lastly, the structure of the methodology can also be interpreted as a prior model update process using new
data in a computationally efficient manner, which makes it highly compatible with the concept of digital twins.

[1] V.-I. Savu, C. Brace, G. Engel, N. Didcock, P. Wilson, E. Kural, and N. Zhang, “Linear Regression-based
Procedures for Extraction of Li-ion Battery Equivalent Circuit Model Parameters,” Batteries, Vol. 10,
No. 10, 343, 2024, doi: 10.3390/batteries10100343

Date of Award	25 Jun 2025
Original language	English
Awarding Institution	University of Bath
Sponsors	AVL List GmbH & Engineering and Physical Sciences Research Council
Supervisor	Chris Brace (Supervisor), Nic Zhang (Supervisor) & Peter Wilson (Supervisor)