Physics-Informed Neural Network with Thevenin Equivalent Circuit for Accurate SOC Li-ion Battery Estimation

Accurate state of charge (SOC) estimation is essential for the safety, performance, and longevity of lithium-ion batteries. Physics-based models such as equivalent circuit models (ECMs) are computationally efficient but struggle under nonlinear and time-varying conditions, whereas purely data-driven approaches often lack interpretability. This study proposes a hybrid framework that integrates a physics-informed neural network (PINN) with a first-order Thevenin ECM for dynamic SOC estimation using only terminal voltage and current inputs. The method incorporates physically derived parameters including open-circuit voltage (OCV), polarization resistance, and capacitance identified through pulse testing. An eighth-order OCV–SOC polynomial regression optimized with a genetic algorithm (GA) enables nonlinear mapping, while the Newton–Raphson (NR) method is applied for final SOC estimation. Experimental validation was performed on 18 Ah lithium iron phosphate (LFP) cells over 300 charge–discharge cycles at 20 °C, extended up to 2000 cycles under 1C/2C rates with cut-off voltages of 3.7 V and 2.7 V. Comparative analysis with extended kalman filters (EKF) and standard neural networks (NN) demonstrates the superiority of the proposed method, achieving a root mean squared error (RMSE) of 0.103, mean absolute percentage error (MAPE) of 0.702%, and coefficient of determination (R²) of 0.998. By embedding physical constraints into the learning process, the PINN enhances accuracy, robustness, and generalizability, while reducing estimation uncertainty, thereby offering a scalable and interpretable solution for real-time battery management systems (BMS) in electric vehicles (EVs) and battery energy storage systems (BESS).