Citation: Navega Vieira, R.; Mauricio
Villanueva, J.M.; Sales Flores, T.K.;
Tavares de Macêdo, E.C. State of
Charge Estimation of Battery Based
on Neural Networks and Adaptive
Strategies with Correntropy. Sensors
2022, 22, 1179. https://doi.org/
10.3390/s22031179
Academic Editor: Junseop Lee
Received: 3 December 2021
Accepted: 21 December 2021
Published: 4 February 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
State of Charge Estimation of Battery Based on Neural
Networks and Adaptive Strategies with Correntropy
Rômulo Navega Vieira * , Juan Moises Mauricio Villanueva , Thommas Kevin Sales Flores
and Euler Cássio Tavares de Macêdo
Renewable and Alternatives Energies Center (CEAR), Electrical Engineering Department (DEE), Campus I,
Federal University of Paraiba (UFPB), Joao Pessoa 58051-900, Brazil; jmauricio@cear.ufpb.br (J.M.M.V.);
thommas.flores@cear.ufpb.br (T.K.S.F.); euler@cear.ufpb.br (E.C.T.d.M.)
* Correspondence: romulo.vieira@cear.ufpb.br; Tel.: +55-83981769614
Abstract:
Nowadays, electric vehicles have gained great popularity due to their performance and
efficiency. Investment in the development of this new technology is justified by increased con-
sciousness of the environmental impacts caused by combustion vehicles such as greenhouse gas
emissions, which have contributed to global warming as well as the depletion of non-oil renewable
energy source. The lithium-ion battery is an appropriate choice for electric vehicles (EVs) due to
its promising features of high voltage, high energy density, low self-discharge, and long life cycles.
In this context, State of Charge (SoC) is one of the vital parameters of the battery management
system (BMS). Nevertheless, because the discharge and charging of battery cells requires complicated
chemical operations, it is therefore hard to determine the state of charge of the battery cell. This
paper analyses the application of Artificial Neural Networks (ANNs) in the estimation of the SoC of
lithium batteries using the NASA’s research center dataset. Normally, the learning of these networks
is performed by some method based on a gradient, having the mean squared error as a cost function.
This paper evaluates the substitution of this traditional function by a measure of similarity of the In-
formation Theory, called the Maximum Correntropy Criterion (MCC). This measure of similarity
allows statistical moments of a higher order to be considered during the training process. For this
reason, it becomes more appropriate for non-Gaussian error distributions and makes training less
sensitive to the presence of outliers. However, this can only be achieved by properly adjusting
the width of the Gaussian kernel of the correntropy. The proper tuning of this parameter is done
using adaptive strategies and genetic algorithms. The proposed identification model was developed
using information for training and validation, using a dataset made available in a online repository
maintained by NASA’s research center. The obtained results demonstrate that the use of correntropy,
as a cost function in the error backpropagation algorithm, makes the identification procedure using
ANN networks more robust when compared to the traditional Mean Squared Error.
Keywords:
estimation; state of charge; batteries; correntropy; cost function; Artificial Neural
Networks
1. Introduction
With the development of electric vehicles, the technologies related to energy manage-
ment systems have been of extreme importance in recent years. One of the main problems
is how to control the process of charging and discharging the battery as well as how to
extend its useful life [
1
]. Lithium-ion batteries, in this context, have been intensely used
in various electric vehicle and renewable energy applications due to their power density
and high energy density, which provides a smaller package volume when compared to
other chemical materials in the construction, as well as intrinsic characteristics associated
with safety, accelerated charging, and longer operational life [
2
]. In electric vehicles (EVs)
or hybrids (HEVs), the battery pack is one of the most essential elements, and because it
is composed of several coupled batteries, there are devices dedicated to monitoring these
Sensors 2022, 22, 1179. https://doi.org/10.3390/s22031179 https://www.mdpi.com/journal/sensors
