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

• Published in: Energies (Basel) 2023-03, Vol.16 (5), p.2218
• Main Authors: da Silva, Cynthia Thamires, Dias, Bruno Martin de Alcântara, Araújo, Rui Esteves, Pellini, Eduardo Lorenzetti, Laganá, Armando Antônio Maria
• Format: Article
• Language: English
• Subjects: Accuracy; Batteries; battery management system; battery models; Boxes; Design of experiments; electric forklift; Energy storage; Experiments; Identification methods; Lithium; Lithium cells; Lithium-ion batteries; Mathematical models; Model accuracy; nonlinear grey box battery model; Optimization; Parameter estimation; Parameter identification; Partial differential equations; Power management; Standard deviation; two-outputs nonlinear grey box model
• ISSN: 1996-1073; 1996-1073
• DOI: 10.3390/en16052218

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.