SOC And SOP Estimation Algorithm Of Ternary Lithium Ion Battery Based On Unscented Kalman Filter

The shortage of fossil energy and the increasingly serious environmental pollution have seriously affected people’s production and life.Therefore,many countries regard electric vehicles as the main development direction of the automobile industry in the future.At present,as the preferred energy source for most electric vehicles,various types of lithium batteries and related technologies of battery management system(BMS)have become a research hotspot,and accurate estimation of state of charge(SOC)is the most basic and important part of BMS.It is very important to accurately estimate the SOC of lithium battery for improving the safety of lithium battery,prolonging the service life of lithium battery and increasing the driving range of electric vehicle.In addition,accurate estimation of state of power(SOP)can allocate lithium battery charge and discharge power more reasonably and improve the performance of electric vehicles.Focusing on the precise estimation of SOC and SOP of lithium batteries,this paper mainly carries out the following work:(1)According to the experimental characteristics of lithium battery,an integer order second order RC equivalent circuit model of lithium battery is introduced.Since actual capacitors have fractional order properties,constant phase angle element is introduced to replace integer order capacitors in the above model,and the fractional second-order RC equivalent circuit model is established.The differential term for solving the fractional order capacitors is defined by Grünwald-Letnikov,and the discrete mathematical equations of the fractional order model are derived.In addition,the nonlinear fitting algorithm based on the Least Square Method(LS)and Adaptive Differential Evolution Algorithm(ADE)were used to identify the above model parameters offline based on the pulse discharge experiment and capacity experiment data at different temperatures.The main idea of LS algorithm is to minimize the sum of the squares of the error of the target quantity,and the optimal solution of model parameters can be obtained when the system noise is characterized by Gaussian white noise.ADE algorithm weighted the sum of the absolute error and the sum of the square error of the target quantity,and set it as the fitness function.The best model parameters were identified through repeated competition to minimize the fitness function value.Compared with LS algorithm,ADE algorithm is much more robust.Experimental results show that the fractional second-order RC equivalent circuit model based on ADE algorithm can better describe the dynamic characteristics of lithium battery in charge and discharge process,the maximum error is less than 50 m V,the average error is less than 5.0m V.(2)In order to solve the SOC estimation problem of nonlinear lithium battery system,square root unscented Kalman filter(SRUKF)is used as estimation algorithm.Compared with the unscented Kalman filter(UKF),SRUKF algorithm obtains the square root of state covariance matrix through QR decomposition and Cholesky decomposition to participate in algorithm iteration,which solves the problem of UKF algorithm collapse due to the loss of non negative qualitative of state covariance matrix.In addition,according to the time-varying characteristics of lithium battery model parameters,this paper uses dual adaptive square root unscented Kalman filter(DSRUKF)to estimate the internal resistance and SOC of lithium battery.Finally,the algorithm is verified by the three dynamic condition experiments at 25℃.Experiments show that based on the same lithium battery model,SRUKF algorithm has high estimation accuracy.The minimum average absolute error,maximum average absolute error,minimum root mean square error and maximum root mean square error of SOC estimation are1.35%,1.62%,2.25% and 2.59%.DSRUKF algorithm can quickly iterate the internal resistance of lithium battery from the wrong initial value to the true value.The minimum average absolute error,maximum average absolute error,minimum root mean square error and maximum root mean square error of SOC estimation are 1.63%,1.95%,2.25% and 3.02%.(3)Based on the fractional second-order RC equivalent circuit model of lithium battery,this paper presents a multi constraint algorithm for estimating the sustained peak power of lithium battery,which takes the current terminal voltage of lithium battery,the real-time estimated SOC and the designed current limit of lithium battery as constraints.The abovementioned SOP estimation algorithm is verified by three dynamic condition experiments at25℃.From the experiments,it can be seen that in different SOC stages,the constraints of continuous charge and discharge current and power are different.The maximum charging and discharging current and power of lithium battery are basically the same in the same length of charging and discharging time,and the maximum discharging power is about 624 W,and the maximum charging power is not more than 159 W.