State Estimation Based On Equilibrium Voltages For Lithium-ion Batteries In Electric Vehicles

The states of a high-power battery mainly contain three items of state-of-charge(SOC), state-of-health(SOH) and state-of-power(SOP), which correspond to the current remaining mileage, the maximum driving range and the instantaneous acceleration ability of a vehicle, respectively. Accurate and reliable estimations of battery states establish a solid basis for ensuring the battery safety, improving the battery efficiency, prolonging the battery lifetime, and optimizing the energy management strategy of a system. However, as the recessive states of a battery, the estimations of SOC, SOH and SOP often depend on the extraction or establishment of the corresponding relationships between the states and internal characteristic parameters of the battery, and these relationships will be affected by the factors such as working conditions, ambient temperatures, aging status and batch difference. Especially when the aging status of the battery are taken into consideration, the establishment of these corresponding relationships will rely on massive prior experiments, which greatly increases the time and social cost for the development and optimization of the state estimation algorithms in battery management systems.Aiming at these problems, the main target of this paper is to realize accurate online estimation of battery states under the precondition of not depending on a large number of prior experiments and data. To achieve such a goal, this paper selects battery’s equilibrium voltages as the characteristic parameters of battery state estimations for the lithium iron phosphate batteries that are most widely used in current applications. Battery’s equilibrium voltage is an external manifestation of the battery’s internal equilibrium state, which is reflected as the stable part of battery’s external voltage, and according to the difference in the acquisition ways and the corresponding internal links, the equilibrium voltages can be subdivided into three types of static equilibrium voltage(i.e., open-circuit voltage, OCV), dynamic equilibrium voltage(DEV) and quasi equilibrium voltage(QEV). By use of a capacity-potential simultaneous coordinate system, the change rules of the equilibrium voltages with battery aging in the vehicle-used stage are analyzed and proved by the correlative theories and experiments, respectively. From this study, it is found that with battery aging, the equilibrium voltage curves only cause the gradual disappearance of voltage platform in the high SOC region, and the corresponding relationship between the equilibrium voltage and battery SOC does not change in the entire SOC range. This characteristic of battery equilibrium voltages provides a solid theoretical support for accurate estimations of the battery states in the whole vehicleused stage, which makes the on-line state estimations can be realized only through the acquisition of the equilibrium voltage curves of the battery at a new state.For the application occasions of battery’s dynamic working conditions, the dynamic equilibrium voltage(DEV) of the battery is selected as the characteristic parameter for the joint estimations of SOC and SOH. On the one hand, the DEV is taken as a function of SOC, and the DEV curve is divided into four sections by the phase transition points of electrode potentials, which are considered as the interval endpoints. Then, a “sectional-conformal” DEV model at normal temperature is established. Based on the model at normal temperature, a complete dynamic equilibrium voltage model is developed by taking the influence of temperatures on the DEV curves into consideration. The new model improves the fitting precision of the equilibrium voltage curve and the adaptability to the actual working temperature, under the precondition of not increasing the calculation complexity. On the other hand, in consideration of the difference between the change rates of the system state and parameter and the dependence of estimation process on preset state noise parameters, the adaptive-state dual extended Kalman filter algorithm based on the statistics of innovation sequence is presented by using maximum likelihood criterion. Based on those mentioned above, in this paper, the state-space equations of the battery states and model parameters are established by mathematical description on battery’s dynamic behavior, and accurate on-line SOC and SOH estimations of the battery throughout the battery lifetime under different temperatures in the vehicle-used stage are realized by use of the equilibrium voltage curves of the battery only at a new state.For the application occasions of battery’s steady working conditions, the static equilibrium voltage(i.e., open-circuit voltage, OCV) of the battery is selected as the core parameter for joint SOC and SOH estimations. To solve the problem of the need of a long-time rest to obtain OCV, based on the experimental investigation and data analysis of voltage relaxation behavior at the battery’s open-circuit status, a definite linear relationship between the polarization relaxation time and the open-circuit time is obtained. Based on this linear relationship, a new voltage relaxation model and a rapid and free-training OCV prediction method are proposed. This method can accurately predict static OCV after full relaxation by collection and calculation of battery voltage data at the initial stage of the battery’s open-circuit status, which can shorten the rest time from traditional 20 h to only 20 min. Meanwhile, the voltage application ranges of this method are calibrated by the analysis of the errors caused by the method in different SOC regions.In order to make best use of battery’s instantaneous charge-discharge capability under dynamic working conditions and guarantee that the battery is always maintained at the peak power state throughout the pulse, the combined currentvoltage limit conditions for battery’s peak power prediction are proposed. Based on the combined limit conditions, the time that the constant current or constant voltage mode accounts for the entire pulse period and the change conditions of the two modes under the corresponding limitations are effectively predicted. By combining these with the online identification method of all the parameters of a battery model, the free-training SOP prediction of the batteries at different temperatures and aging levels is realized without dependency on any prior experiments and knowledge.