A physically inspired equivalent neural network circuit model for SoC estimation of electrochemical cells

Battery Management System (BMS) design for Lithium-ion batteries State of Charge (SoC) prediction has a crucial role in Electric Vehicles (EVs) and smart grids development. The need to design compact, light and fast devices requires finding a suitable trade-off between effectiveness and efficiency. In the literature, it is well emphasized that the application of electrochemical-based methods such as the Pseudo-Two-Dimensional (P2D) model is computationally prohibitive and requires significant simplifications. Conversely, plain Equivalent Circuit Models (ECM) are too simple and unable to represent the cell dynamics. The application of an Ensemble Neural Network (ENN) as Equivalent Neural Network Circuit (ENNC) emerged as a promising solution able to synthesize expressive and computationally efficient models. Indeed, with the support of a suitable dataset, an ENN can be configured to represent a given ECM, modeling each lumped parameter through an assigned Neural Network (NN). Accordingly, the ENNC system is able to keep a physical description of the battery cell while approximating the non-linear dynamic of each component. The paper proposes a novel ENNC battery named Physical Inspired-Equivalent Neural Network Circuit (PI-ENNC) whose ensemble architecture relies on a fractional-order Extended Single Particle (ESP) Lithium-ion cell formulation. The PI-ENNC is designed to approximate the ESP transfer functions referred to the ohmic effects, the electrolyte diffusion and the non-uniform charge distribution in the cell. The proposed model has been tested with three publicly available datasets, investigating the model behavior according to two different training strategies and with different input configurations. In order to prove its effectiveness, results have been compared with a simpler version proposed in a previous work. Results highlight the effectiveness of PI-ENNC in SoC prediction, underlining the importance of designing an ENN architecture that leverages on equations and constraints that reflect the physical phenomena of the cell.