Accurate determination of the performance and precise prediction of the state of health (SOH) of lithium-ion batteries are necessary to ensure reliability and efficiency in real-world application. However, most SOH offline studies were based on dynamic stress tests, which only reflect the universal rule of degradation, but are not necessarily applicable for real-world applications. This paper presents an experimental evaluation of two different operations of real-world plug-in hybrid electric vehicles with LiFePO₄ batteries as energy-storage systems. First, the LiFePO₄ batteries were subjected to a set of comparative experimental tests that consider the effects of charge depleting (CD) and charge sustaining (CS) operations. Then, different voltage analysis along with the close-to-equilibrium open circle voltage was utilized to evaluate the performance of the batteries in life cycles. Finally, a qualitative relationship between the external factors (the percentage of time of CD/CS operations during the entire driving range) and the degradation mechanism was built with the help of the proposed methods. Results indicated that the external factors affect the degree of the batteries degradation, but not up to the point when the capacity fading stage occurs. This relationship contributes to the foundation for plug-in hybrid electric vehicles’ (PHEVs’) energy management strategy or battery management system control strategy.

A triple polarization (TP) model is proposed based on the second-order RC hysteresis equivalent circuit model, in order to more precisely reflect the dynamic and static characteristics of a LiFePO₄ (LFP) battery, considering the long relaxation time and overshoot of its polarization voltage. The TP model introduces an RC link, whose time constant varies with changes in the battery operating status to represent the fast build-up and slow relaxation of the polarization voltage. Specifically, such an RC link evolves into an RLC parallel link during charging to reveal the overshoot characteristic. In this way, the external characteristics of LFP batteries, considering the complex phase transition process, are simulated by a simple equivalent circuit. Constant-current pulse tests are performed to verify the proposed model. For application, a state-of-charge (SOC) estimation is implemented on the basis of the TP model, with the use of a transformed cubature Kalman Filter (TCKF). The experimental results show that the TP model is able to represent the dynamic and static characteristics, as well as estimate the SOC of an LFP battery with a good accuracy.

The mass transfer in lithium-ion batteries is a low-frequency dynamic that affects their voltage and performance. To find an effective way to describe the mass transfer in lithium-ion batteries, a simplified electrochemical lithium-ion battery model based on ensemble learning is proposed. The proposed model simplifies lithium-ion transfer in electrode particles with ensemble learning which ensembles discrete-time realization algorithm (DRA), fractional-order Padé approximation model (FOM), and three parameters (TPM) parabolic. The lithium-ion transfer in the electrolyte is simplified by the first-order inertial element (FIE). The results show that the proposed model achieves not only accurate lithium-ion concentration prediction in solid and electrolyte phase but also precise voltage prediction with low computational complexity.