This paper presents an accurate state of charge (SOC) estimation algorithm using a recurrent neural network with long short-term memory (LSTM) for lithium-ion batteries (LIB) performing under real conditions. With its self-learning ability, this data-driven approach is able to model the highly non-linear behavior of LIB due to changes of environment and working conditions all along the battery lifetime. It is shown that the LSTM approach outperforms common physical-based models using Extended Kalman Filters (EKF) regarding accuracy and stability. To demonstrate this benefit for real-world applications, the provided network is trained and tested with data gathered from commercial industry applications in the domain of energy storage. The LSTM is evaluated and compared with an equivalent circuit model (ECM) using EKF under different working conditions. For dynamic loading profiles, the ECM-EKF achieves an error (RMSE) of 9.5% whereas the LSTM achieves an error (RMSE) of 5.0%.

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Krylov-based methods are an attractive alternative to traditional fixed-point iterative schemes, being much more robust and accurate when solving elliptic equations (e.g., the energy equation in the solid domain). This study assesses the performance of a Krylov-based accelerator, when used for Conjugate Heat Transfer (CHT) simulations of an electrical battery-pack. The non-linear nature of CHT simulations (due to spatial & temporal changes in boundary conditions) necessitates the use of the non-linear form of the Krylov-based accelerator (termed NKA). NKA is used while performing steady-state CHT simulations of an air-cooled Lithium-ion battery-pack, specifically to help accelerate the solution of the solid-domain energy equation. The effect of using either isotropic or anisotropic thermal conductivity within the cylindrical Lithium-ion battery cells is also evaluated. Results obtained using the NKA accelerator are compared, in terms of accuracy and speed, to those obtained from a traditional non-linear fixed-point iterative scheme based on Successive Over-Relaxation (SOR). The NKA accelerator is found to perform quite well for the problem at hand, providing results with the specified accuracy, while also being between 5 and 20 times faster than SOR (while solving the solid energy equation). The robust nature of NKA also leads to better global heat-balance within the battery-pack at all times during the simulation. Overall, computational cost reductions of 30% to 40% are observed when using NKA for the battery-pack simulations.

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