Two-Outputs Nonlinear Grey Box Model for Lithium-Ion Batteries

Cynthia Thamires da Silva, Bruno Martin de Alcântara Dias, Rui Esteves Araújo (), Eduardo Lorenzetti Pellini and Armando Antônio Maria Laganá
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Cynthia Thamires da Silva: PEA—Polytechnic School (POLI-USP), University of São Paulo, São Paulo 05508-010, Brazil
Bruno Martin de Alcântara Dias: PEA—Polytechnic School (POLI-USP), University of São Paulo, São Paulo 05508-010, Brazil
Rui Esteves Araújo: INESC TEC and Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal
Eduardo Lorenzetti Pellini: PEA—Polytechnic School (POLI-USP), University of São Paulo, São Paulo 05508-010, Brazil
Armando Antônio Maria Laganá: PEA—Polytechnic School (POLI-USP), University of São Paulo, São Paulo 05508-010, Brazil

Energies, 2023, vol. 16, issue 5, 1-15

Abstract: Storing energy efficiently is one of the main factors of a more sustainable world. The battey management system in energy storage plays an extremely important role in ensuring these systems’ efficiency, safety, and performance. This battery management system is capable of estimating the battery states, which are used to give better efficiency, a long life cycle, and safety. However, these states cannot be measured directly and must be estimated indirectly using battery models. Therefore, accurate battery models are essential for battery management systems implementation. One of these models is the nonlinear grey box model, which is easy to implement in embedded systems and has good accuracy when used with a good parameter identification method. Regarding the parameter identification methods, the nonlinear least square optimization is the most used method. However, to have accurate results, it is necessary to define the system’s initial states, which is not an easy task. This paper presents a two-outputs nonlinear grey box battery model. The first output is the battery voltage, and the second output is the battery state of charge. The second output was added to improve the system’s initial states identification and consequently improve the identified parameter accuracy. The model was estimated with the best experiment design, which was defined considering a comparison between seven different experiment designs regarding the fit to validation data, the parameter standard deviation, and the output variance. This paper also presents a method for defining a weight between the outputs, considering a greater weight in the output with greater model confidence. With this approach, it was possible to reach a value 1000 times smaller in the parameter standard deviation with a non-biased and little model prediction error when compared to the commonly used one-output nonlinear grey box model.

Keywords: battery models; battery management system; nonlinear grey box battery model; two-outputs nonlinear grey box model; electric forklift (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
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