A Probabilistic Fractional Order Physics Informed Mamba Kolmogorov‐Arnold Network for State‐of‐Charge Estimation in Grid‐Connected Battery Energy Storage Systems

Accurate state of charge (SOC) estimation is critical for reliable battery energy storage system (BESS) operation in renewable grids. However, conventional integer‐order and deterministic models often fail to capture long‐memory electrochemical diffusion or quantify uncertainty under dynamic conditions. To address this, this paper proposes the probabilistic fractional‐order Mamba Kolmogorov‐Arnold network (PFO‐Mam‐KAN) framework. This architecture uniquely integrates a linear‐complexity temporal Mamba encoder to efficiently model long sequences, a probabilistic KAN decoder for estimating time‐varying parameter distributions, and a differentiable fractional‐order physics layer using constant phase elements, to capture non‐Markovian dynamics. These components are unified via an adaptive Kalman‐gated correction mechanism that dynamically modulates reliance on measurements based on propagated uncertainty. Validated on a hybrid AC/DC microgrid using the Sandia database, the framework achieves a superior SOC estimation RMSE of 0.31% and MAE of 0.18%, outperforming contemporary advanced observers. The model demonstrates improved SOC estimation under 3% measurement noise and temperature variations (10°C‐40°C), while exhibiting less computation burden.