A battery’s state-of-power (SOP) refers to the maximum power that can be extracted from the battery within a short period of time (e.g., 10 s or 30 s). However, as its use in applications is growing, such as in automatic cars, the ability to predict a longer usage time is required. To be able to do this, two issues should be considered: (1) the influence of both the ambient temperature and the rise in temperature caused by Joule heat, and (2) the influence of changes in the state of charge (SOC). In response, we propose the use of a model-based extreme learning machine (Model-ELM, MELM) to predict the battery future voltage, power, and surface temperature for any given load current. The standard ELM is a kind of single-layer feedforward network (SLFN). We propose using a set of rough models to replace the active functions (such as logsig()) in the ELM for better generalization performance. The model parameters and initial SOC in these “rough models” are randomly selected within a given range, so little prior knowledge about the battery is required. Moreover, the identification of the complex nonlinear system can be transferred into a standard least squares problem, which is suitable for online applications. The proposed method was tested and compared with RLS (Recursive Least Square)-based methods at different ambient temperatures to verify its superiority. The temperature prediction accuracy is higher than ±1.5 °C, and the RMSE (Root Mean Square Error) of the power prediction is less than 0.25 W. It should be noted that the accuracy of the proposed method does not rely on the accuracy of the state estimation such as SOC, thereby improving its robustness.

A battery’s state-of-charge (SOC) can be used to estimate the mileage an electric vehicle (EV) can travel. It is desirable to make such an estimation not only accurate, but also economical in computation, so that the battery management system (BMS) can be cost-effective in its implementation. Existing computationally-efficient SOC estimation algorithms, such as the Luenberger observer, suffer from low accuracy and require tuning of the feedback gain by trial-and-error. In this study, an algorithm named lazy-extended Kalman filter (LEKF) is proposed, to allow the Luenberger observer to learn periodically from the extended Kalman filter (EKF) and solve the problems, while maintaining computational efficiency. We demonstrated the effectiveness and high performance of LEKF by both numerical simulation and experiments under different load conditions. The results show that LEKF can have 50% less computational complexity than the conventional EKF and a near-optimal estimation error of less than 2%.