An Adaptive Approach for Battery State of Charge and State of Power Co-Estimation With a Fractional-Order Multi-Model System Considering Temperatures

State of charge (SOC) and state of power (SOP) are two critical indices for lithium-ion batteries. Due to the complex operating environment in real applications, battery temperature can change significantly. This will lead to varied battery internal characteristics and pose a challenge for battery modelling and state estimation. This paper proposes an adaptive approach for battery online SOC and SOP co-estimation considering temperatures. First, a fractional-order multi-model system (FO-MMS) is constructed by integrating three sub-models at −5 Celsius, 20 Celsius, and 45 Celsius. To accommodate the battery current-voltage behaviors at different loads, SOCs, and temperatures, the contribution coefficient of each sub-model is adapted online through a temperature-embedded regularized moving horizon estimation algorithm. Second, a fractional-order multi-model proportional-integral observer (FO-MM-PIO) is designed for SOC estimation which achieves rapid convergence and suppresses external disturbances using the H-infinity criteria. Moreover, the nonlinear charge transfer dynamics of a battery under intense loads is simulated through the Butler-Volmer equation. An iterative approaching algorithm is then derived to estimate battery SOP in high fidelity. The experimental validations demonstrate that the proposed co-estimation method achieves the mean absolute error of less than 1.3% in SOC estimation and 2 W in SOP estimation, even at a sub-zero temperature (i.e., −5 Celsius).