基于双自适应扩展粒子滤波器的锂离子电池状态联合估计

Nowadays, it is necessary for Lithium-ion batteries to realize accurate estimation of state of charge (SOC) and state of health (SOH) for improvement in energy management, utilization efficiency, and safety performance. The particle filter is widely used in estimates of SOC and SOH. Particles are generated and recursively updated from a nonlinear process model, thus accurately characterizing the nonlinear characteristics of the battery. However, the basic particle filter suffers from particle degeneracy, where most particle weights approach to zero and contribute little to further estimation. Furthermore, as batteries age, estimation error increases due to parameter changes in the battery model if not updated in time. Therefore, this paper proposes the dual adaptive extended particle filter (DAEPF) based on the fractional-order battery model. State estimation accuracy is utilized to adjust noise covariance adaptively, and the extended Kalman filter (EKF) realizes local linearization of the particle distribution function. SOC and SOH are simultaneously estimated at different time steps so that the aging effect of parameters on SOC estimation is avoided with a low computation burden. Firstly, this study establishes the factional-order equivalent circuit model, which replaces integer-order capacitors with constant phase elements. The parameters in the proposed model are identified by an adaptive genetic algorithm, proving that the factional-order model has a lower error when estimating terminal voltage. Secondly, considering the balance between convergence rate and estimation accuracy, the noise covariance of the system is adaptively adjusted according to the prior and the posterior estimates. Thirdly, the proposal distribution is obtained by local linearization, and the extended Kalman filter is utilized to compute the expectation and variance of normally distributed particles. As a result, the particle distribution is closer to the actual value, and the weights of particles are updated in real time. Finally, the SOC and SOH of the Lithium-ion battery are estimated by two particle filters, one for SOC estimation and the other for parameter estimation. With battery parameters updated constantly, the SOC estimation is improved under different working conditions. In the pulse discharge test, the mean absolute error in the estimated terminal voltage of the fractional-order circuit model is only 0.005 2 V, 22.4% lower than the integer model. The UDDS test verifies the effectiveness of the proposed joint-estimation algorithm. The results show that DAEPF can estimate SOC in less than 151 seconds with a maximum error of 1.35%, mean absolute error of 0.39%, and root-mean-square error of 0.48%, all lower than the single filter. Moreover, as SOC is estimated in the state filter, SOH is computed with a larger time step in the parameter filter whose mean absolute error is lower than 0.5%. The conclusions of this study are as follows: (1) Compared with the integer-order circuit model, the factional-order circuit model can better describe the dynamic process of the battery with lower estimation error in terminal voltage. (2) The noise covariance should be adjusted based on the difference between the prior and posterior estimates. (3) The extended Kalman filter is suitable for local linearization of the proposed distribution of particles, which assumes a normal distribution of particles and gives expectation and variance of the distribution. (4) Joint estimation of SOC and SOH by the developed particle filters can update battery parameters in time and thus improve SOC estimation accuracy. In return, the new states are fed into the parameter filter for further estimation. The test results demonstrate that DAEPF achieves higher estimation accuracy and a faster convergence rate.