Convergence Study And Application Of Joint Parameter And State Estimation For Lithium-ion Batteries

Accurate estimation of the state of a power battery is the key to ensuring its stable operation.Model-based state estimation has been extensively studied and the accuracy of the model determines the accuracy of the state estimation.The accuracy of the model determines the accuracy of the state estimation.The parameters of the battery vary with temperature,state of charge and state of health,etc.Online identification of the battery parameters is an effective method to ensure the accuracy of the model.There have been many studies on joint parameter and state estimation algorithms in the industry,and the algorithms with fast convergence and good robustness under specific working conditions emerge endlessly.However,few studies have theoretically analyzed the convergence of joint parameter and state estimators.The parameter/state estimator is essentially an error correction system,and the estimation algorithm is only part of the system,convergence of the estimation algorithm does not mean convergence of the estimation error.To explore the convergence of the estimation error,it is necessary to study the dynamic and steady-state characteristics of the estimator.In this context,this paper investigates the error convergence of three kinds of joint estimators based on a first-order RC equivalent circuit model.First,the error state equations of the state estimator and the three kinds of parameter estimators based on the first-order RC equivalent circuit model in existing studies are derived,and the stability of each estimator is analyzed by Lyapunov’s second method.The analysis results show that the state estimator is a stable system,the parameter estimator is dynamically stable under changing inputs and the stability of these estimators does not change due to external disturbances.The dynamic process of the convergence of the errors of single estimator is analyzed in conjunction with the parameter/state error state equation and Lyapunov’s second method,and verified by simulation.Secondly,the error characteristics when the dual estimator joint estimating with external disturbances are analyzed,and the steady-state error expression of the state estimator is deduced in this case,and the influence of the external error disturbance on the steady-state error of the parameters is qualitatively analyzed.Expressions for the Cramer-Rao(CR)bound for each parameter in the three kinds of parameter estimators are derived,and the steady-state error of each parameter is quantitatively analyzed.Combined with the simulation,it is further found that the actual error size of the parameters mainly depends on the degree of error convergence.By analyzing the relationship between the numerical value of each component of the parametric Cramer-Rao boundary expression and the actual error of the parameter,it is found that the degree of convergence of the parameter error is positively correlated with the orthogonality between the input vectors of the parameter estimator.A method for screening high-precision parameter identification results by orthogonality between vectors.Finally,the feasibility of the polarization parameter data-driven model trained by the estimation results which screened by the orthogonality between the input vectors of the parameter estimator is tested.The parameter and state estimation results are obtained through experiments and real scene simulations,respectively,and these estimation results are screened by the proposed method and then used to train the polarization parameter data-driven model.The datadriven model is combined with the state estimator and tested under ten operating conditions,three temperature and capacity error conditions.The test results show that the polarization parameter data-driven model can improve the SoC estimation accuracy.