SOC Estimation for Lithium-Ion Batteries in Electric Tractors Under Variable Temperature and Field Conditions Using a GRU-FOEKF Method

Accurate state of charge (SOC) estimation is essential for the reliable operation and energy management of electric agricultural machinery, particularly electric tractors operating under complex field conditions. This study aims to improve SOC estimation accuracy and robustness by proposing a hybrid method that integrates a gated recurrent unit (GRU) neural network with a fractional-order extended Kalman filter (FOEKF). The GRU model is employed to capture the nonlinear behavior of lithium-ion batteries, while the FOEKF is used to mitigate noise and compensate for model uncertainties, forming a coupled data-driven and model-based framework. Experiments were conducted on lithium-ion batteries for electric tractors under hybrid pulse power characterization (HPPC) conditions at 15 °C, 25 °C, and 35 °C. These experiments can effectively simulate the dynamic power fluctuation characteristics of the battery caused by variations in electric tractor operating conditions during agricultural operations in different seasons. Experimental results demonstrate that, compared with conventional GRU and FOEKF methods, the proposed GRU-FOEKF method achieves lower estimation errors and improved robustness. In particular, at 25 °C, the proposed method achieves an MAE of 0.9% and an RMSE of 1.1%, outperforming the compared algorithms. These findings indicate that the proposed strategy is a feasible and effective solution for battery management systems in electric agricultural machinery, contributing to the development of smart and sustainable agriculture.