Fractional-Order Model-Based State-of-Charge and State-of-Power Estimation with Available-Capacity Feedback for Lithium-ion Batteries

Accurate state-of-charge (SOC) and state-of-power (SOP) estimation requires consistent treatment of voltage dynamics and available-capacity uncertainty. This study couples a fractional-order equivalent circuit model, a fast multi-innovation unscented Kalman filter SOC observer, and a slow capacity estimator. Self-adaptive learning particle swarm optimization (SLPSO) identifies the model parameters. Capacity feedback links SOC correction to voltage prediction and multi-constraint SOP calculation, with constant-power discharge verification. Compared with a second-order resistor-capacitor model, the fractional-order model reduces voltage root-mean-square error (RMSE) and mean absolute error by 3.45% and 5.82%, respectively. SLPSO reduces the mean final voltage RMSE from 2.215 to 1.561 mV. Across two dynamic profiles and initial SOC values of 0.90 to 1.05, the proposed method yields SOC RMSE values of 0.844% to 0.966%. The fixed-capacity baseline yields 4.9% to 9.8% under initial-SOC mismatch. The maximum capacity-related state-of-health indicator deviation remains below 0.279 percentage points. The maximum discharge-power error is 2.20% for 10 s and below 5% for all 30 s cases. It reaches 8.34% at 30% SOC for 60 s, indicating the need for caution under low-SOC, long-duration operation. These results are limited to fresh-cell tests at 25 °C.