With rapid transportation electrification worldwide, lithium-ion batteries have gained much attention for energy storage in electric vehicles (EVs). State of power (SOP) is one of the key states of lithium-ion batteries for EVs to optimise power flow, thereby requiring accurate online estimation. Equivalent circuit model (ECM)-based methods are considered as the mainstream technique for online SOP estimation. They primarily vary in their basic principle, technical contribution, and validation approach, which have not been systematically reviewed. This paper provides an overview of the improvements on ECM-based online SOP estimation methods in the past decade. Firstly, online SOP estimation methods are briefed, in terms of different operation modes, and their main pros and cons are also analysed accordingly. Secondly, technical contributions are reviewed from three aspects: battery modelling, online parameters identification, and SOP estimation. Thirdly, SOP testing methods are discussed, according to their accuracy and efficiency. Finally, the challenges and outlooks are presented to inspire researchers in this field for further developments in the future.

In this article, a fractional-order model (FOM)-based online state of charge (SOC) and state of power (SOP) estimation method is proposed for lithium-ion batteries in electric vehicles. First, the model parameters of a second-order FOM are globally optimized under the dynamic stress test profile, where two resistor-constant phase element networks are recognized to represent battery internal dynamics at different timescales. Second, to enhance the model performance in SOC and SOP estimation, a partial-adaptive FOM (PA-FOM) is realized by fixing the parameters of the first resistor-constant phase element network with slow dynamics while allowing the online adaption of the second resistor-constant phase element network with fast dynamics. Based on the PA-FOM, online SOC estimation is implemented using an adaptive extended Kalman filter algorithm while an unscented Kalman filter-based iterative approaching algorithm is devised to estimate SOP. The proposed method is validated under different EV driving profiles. The experimental results show that the PA-FOM has an outstanding performance in interpreting battery dynamics at different timescales and the proposed SOC and SOP estimation method is highly accurate and efficient.

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).