Online parameters identification and state of charge estimation for lithium‐ion batteries using improved adaptive dual unscented Kalman filter

State of charge (SOC) is a vital parameter which helps make full use of battery capacity and improve battery safety control. In this paper, an improved adaptive dual unscented Kalman filter (ADUKF) algorithm is adopted to realize co‐estimation of the battery model parameters and SOC. Notably, the covariance matching method that can adapt the system noise covariance and the measurement noise covariance is used to improve the estimation accuracy. Besides, singular value decomposition (SVD) is utilized to deal with the non‐positive error covariance matrix in both unscented Kalman filters, further enhancing the stability of estimation algorithm. Verification results under Dynamic Stress test and Federal Urban Driving Schedule test indicate that improved ADUKF can achieve more accurate SOC estimates with error band controlled within 2.8%, while that of traditional dual unscented Kalman filter (DUKF) can only be controlled within 5%. Moreover, robustness analysis is also conducted and the validation results present that the proposed algorithm can still provide precise SOC prediction results under some disturbances, such as erroneous initial SOC, inaccurate battery capacity, and various ambient temperatures.     

A wavelet transform‐adaptive unscented Kalman filter approach for state of charge estimation of LiFePo4 battery

LiFePo₄ battery is widely used in electric vehicles; however, its flatness and hysteresis of the open‐circuit voltage curve pose a big challenge to precise state of charge (SOC) estimation. The issue is discussed and addressed in this paper. First, a cell model with hysteresis is built to describe real‐time dynamic characteristics of the LiFePo₄ battery. Second, the model parameters and SOC are estimated independently to avoid the possibility of cross interference between them. For model identification, an adaptive unscented Kalman filter (AUKF) algorithm is used to identify the cell parameters as they change slowly. While SOC could change rapidly, wavelet transform AUKF algorithm is put forward to estimate SOC. In the novel algorithm, the measurement noise can be estimated and updated online. Finally, the performance of the proposed method is verified under dynamic current condition. The experimental results show that estimated value based on the proposed method is more accurate than unscented Kalman filter‐based method and AUKF‐based algorithm. Meanwhile, the proposed estimator also has the merits of fast convergence and good robustness against the initialization uncertainty.     

State of charge estimation for lithium-ion battery based on an intelligent adaptive unscented Kalman filter

Adaptive unscented Kalman filter (AUKF) has been widely used for state of charge (SOC) estimation of lithium-ion battery. The noise covariance of the conventional AUKF method is updated based on the innovation covariance matrix (ICM), which is estimated using the error innovation sequence (EIS). However, the distribution of EIS changes due to the time-varying noise, load current dynamics and modelling error, which will lead to inaccurate ICM estimation. Therefore, an intelligent adaptive unscented Kalman filter (IAUKF) method is proposed to detect the distribution change of EIS. Then, the ICM is estimated based on the EIS after the distribution change. Results show that the IAUKF method can improve SOC estimation accuracy significantly. Compared with that of the AUKF method, the root mean squared error and the mean absolute error of SOC based on the IAUKF method decrease by 43.70% and 72.37% under random walk discharge condition, respectively. In addition, the computation time of the IAUKF method slightly increases by 6.27% compared with that of AUKF method. Finally, the effect of initial parameters on the SOC estimation accuracy was analysed. The results indicate that proper algorithm tuning, such as initial window length of EIS for ICM update and the threshold value, can further improve the SOC accuracy based on the proposed IAUKF method. The proposed IAUKF method also shows high robustness against initial measurement noise covariance.     

Fractional‐order modeling and SOC estimation of lithium‐ion battery considering capacity loss

For state‐of‐charge (SOC) estimation, the resistance deterioration and continuous capacity loss can lead to erroneous estimation results. In this paper, an SOC estimator of lithium‐ion battery based on the fractional‐order model and adaptive dual Kalman filtering algorithm is proposed first. Then, to improve the accuracy of SOC estimation considering capacity loss, the particle filter algorithm is applied to update capacity online in real time. Then, an SOC estimation method is proposed considering battery capacity loss. The simulation results show that the accuracy of battery capacity prediction based on particle filter is high under the condition of capacity loss.     

A normal-gamma-based adaptive dual unscented Kalman filter for battery parameters and state-of-charge estimation with heavy-tailed measurement noise

This study simultaneously considers the state-of-charge (SOC) estimation and model parameter identification of lithium-ion batteries with outliers in measurements. Conventional Kalman-type filters may degrade performance in this case since they assume Gaussian-distributed measurement noise. To improve the SOC estimation accuracy under this condition, a robust normal-gamma (NG)-based adaptive dual unscented Kalman filter (NG-ADUKF) is proposed. First, by modeling the joint distribution of the state and auxiliary variables of the measurement noise as the NG distribution, the unscented Kalman filter (UKF) is integrated with the NG filter to deal with the heavy-tailed measurement noise. Second, the online parameter identification and SOC estimation are realized simultaneously by alternatively using two NG-based adaptive UKFs. The performance of the proposed algorithm is validated by the New European Driving Cycle and Urban Dynamometer Driving Schedule tests. Experimental results show that the proposed NG-ADUKF algorithm has more accurate SOC estimations compared with the dual UKF (DUKF) and the variational Bayes-based adaptive DUKF (VB-ADUKF) in the case of mistuning and outliers. Moreover, the proposed method is more computationally efficient than VB-ADUKF.     

Dynamic mechanical behavior of prismatic lithium‐ion battery upon impact

Dynamic impact safety of lithium‐ion batteries (LIBs) is a hot subject. The mechanical‐electrical behavior of LIBs under dynamic loading was studied in this study. Drop‐weight tests of two types of indenter, namely, round and flat heads, were conducted. Strain rate and state of charge (SOC) effects on the mechanical properties of LIBs under different indenters were fully discussed. The interaction between mechanical performance and electrical behavior was studied. Experiments show that the structural stiffness of batteries increases with strain rate increase but exhibits little effect from SOC. Different indenters have a significant influence on the mechanical behavior of the prismatic LIBs. Under the same impact rate and SOC, the peak load of a flat head is considerably larger than that of a round head. The battery exhibits a hard short‐circuit under the impact of a round head and a soft short‐circuit under the impact of a flat head. This result shows that the larger the contact area between the indenter and the battery is, the larger the impact load under the same drop‐weight and impact rate will be, although the impact safety of the battery does not decrease. The results provide useful insights into the basic understanding of the electromechanical coupling integrity of LIBs.     

State‐of‐charge estimation of power lithium‐ion batteries based on an embedded micro control unit using a square root cubature Kalman filter at various ambient temperatures

The development of a novel method to estimate the state of charge (SOC) with low read‐only memory (ROM) occupancy, high stability, and high anti‐interference capability is very important for the battery management system (BMS) in actual electric vehicles. This paper proposes the square root cubature Kalman filter (SRCKF) with a temperature correction rule, based on the BMS of a common on‐board embedded micro control unit (MCU), to achieve smooth estimation of SOC. The temperature correction rule is able to reduce the testing effort and ROM space used for data table storage (189.3 kilobytes is much smaller than the storage of the MPC5604B, with 1000 kilobytes), while the SRCKF is adopted to achieve highly robust real‐time SOC estimation with high resistance to interference and moderate computing cost (68.3% of the load rate of the MPC5604B). The results of multiple experiments show that the proposed method with less computational complexity converges rapidly (in approximately 2.5 s) and estimates the SOC of the battery accurately under dynamic temperature condition. Moreover, the SRCKF algorithm is not sensitive to the high measuring interference and highly nonlinear working conditions (even with 1% current and voltage measurement disturbances, the root mean square error of the proposed method can be as high as 0.679%).     

Parameter estimation of an electrochemistry‐based lithium‐ion battery model using a two‐step procedure and a parameter sensitivity analysis

Lithium‐ion batteries are indispensable in various applications owing to their high specific energy and long service life. Lithium‐ion battery models are used for investigating the behavior of the battery and enabling power control in applications. The Doyle‐Fuller‐Newman (DFN) model is a popular electrochemistry‐based model, which characterizes the dynamics in the battery through diffusions in solid and electrolyte and predicts current/voltage response. However, the DFN model contains a large number of parameters that need to be estimated to obtain an accurate battery model. In this paper, a computationally feasible two‐step estimation approach is proposed that only uses voltage and current measurements of the battery under consideration. In the two‐step procedure, the parameters are divided into 2 groups. The first group contains thermodynamic parameters, which are estimated using low‐current discharges, while the second group contains kinetic parameters, which are estimated using a well‐designed highly‐dynamic pulse (dis‐)charge current. A parameter sensitivity analysis is done to find a subset of parameters that can be reliably estimated using current and voltage measurements only. Experimental data are collected for 12 Ah nickel cobalt aluminum pouch lithium‐ion cell. The voltage predictions of the identified model are compared with several experimental data sets to validate the model. A root mean square error between model predictions and experimental data smaller than 16 mV is achieved.     

A graphical model for evaluating the status of series‐connected lithium‐ion battery pack

State evaluation of battery pack is essential for battery management but laborious when dealing with massive information of cells within the pack. A graphical model for evaluating the status of series‐connected Li‐ion battery pack is established to release the burden. The model is founded by a 2D diagram, with the electric quantity “E” and the capacity “Q” as its axes, therefore called by the “E‐Q diagram.” The new graphical diagram presents the dynamics of cell variations in a linear way, thereby benefiting the design and management of battery pack, including (1) quantifying the cell variations by region, (2) illustrating the evolution of cell variations during aging, (3) guiding the estimation of pack states considering algorithm error in cell states, and (4) solving the balancing problem. The experimental results conform to the theoretical analysis, indicating that the E‐Q diagram will be pervasively applied in the design and management of series‐connected battery pack. Moreover, the E‐Q diagram is suitable for education on the basics of a battery pack, because it is a graphical model.     

Thermal management system of lithium‐ion battery module based on micro heat pipe array

Temperature affects the performance of electric vehicle battery. To solve this problem, micro heat pipe arrays are utilized in a thermal management system that cools and heats battery modules. In the present study, the heat generation of a battery module during a charge‐discharge cycle under a constant current of 36 A (2C) was computed. Then, the cooling area of the condenser was calculated and experimentally validated. At rates of 1C and 2C, the thermal management system effectively reduced the temperature of the module to less than 40°C, and the temperature difference was controlled less than 5°C between battery surfaces of the module. A heating plate with 30‐W power effectively improved charge performance at low temperature within a short heating time and with uniform temperature distribution. Charge capacity obviously increased after heating when battery temperature was below 0°C. This study presents a new way to enhance the stability and safety of a battery module during the continuous charge‐discharge cycle at high temperatures and low temperatures accordingly.     

A model‐based and data‐driven joint method for state‐of‐health estimation of lithium‐ion battery in electric vehicles

Lithium‐ion battery state‐of‐health estimation is one of the vital issues for electric vehicle safety. In this work, a joint model‐based and data‐driven estimator is developed to achieve accurate and reliable state‐of‐health estimation. In the estimator, an increase in ohmic resistance extracted from the Thevenin model is defined as the health indicator to quantify the capacity degradation. Then, a linear state‐space representation is constructed based on the data‐driven linear regression. Furthermore, the Kalman filter is introduced to trace capacity degradation based on the novel state space representation. A series of battery aging datasets with different dynamic loading profiles and temperatures are obtained to demonstrate the accuracy and robustness of the proposed method. Results show that the maximum error of the Kalman filter is 2.12% at different temperatures, which proves the effectiveness of the proposed method.     

State of charge estimation method based on the extended Kalman filter algorithm with consideration of time-varying battery parameters

In developing battery management systems, estimating state-of-charge (SOC) is important yet challenging. Compared with traditional SOC estimation methods (eg, the ampere-hour integration method), extended Kalman filter (EKF) algorithm does not depend on the initial value of SOC and has no accumulated error, which is suitable for the actual working condition of electric vehicles. EKF is a model-based algorithm; the accuracy of SOC estimated by this algorithm was greatly influenced by the accuracy of battery model and model parameters. The parameters of battery change with many factors and exhibit strong nonlinearity and time variance. Typical EKF algorithm approximates battery as a linear, time-invariant system; however, this approach introduces estimation errors. To minimize such errors, previous studies have focused on improving the accuracy of identifying battery parameters. Although studies on battery model with time-varying parameters have been carried out, few have studied the combination of time-varying battery parameters and EKF algorithm. A SOC estimation method that combines time-varying battery parameters with EKF algorithm is proposed to improve the accuracy of SOC estimation. Battery parameter data were obtained experimentally under different temperatures, SOC levels, and discharge rates. The results of parameter identification are made into a data table, and the battery parameters in the EKF system matrix are updated by looking up the data in the table. Simulation and experimental results shown that, average error of SOC estimated by the proposed algorithm is 2.39% under 0.9 C constant current discharge and 2.4% under 1.3 C, which is 1.91% and 2.35% lower than that of EKF algorithm with fixed battery parameters. Under intermittent discharge with constant current (1.1 C) and capacity (10%), the average error of SOC estimated by the proposed algorithm is 1.4%, which is 0.3% lower than that of EKF algorithm with fixed battery parameters. The average error of SOC estimated by the proposed algorithm under the New European Driving Cycle (NEDC) is 1.6%, which is 0.2% lower than that of EKF algorithm with fixed battery parameters. Relative to the EKF algorithm with fixed battery parameters, the proposed EFK algorithm with time-varying battery parameters yields higher accuracy.     

A hybrid lithium‐ion battery model for system‐level analyses

We describe an advanced lithium‐ion battery model for system‐level analyses such as electric vehicle fleet simulation or distributed energy storage applications. The model combines an empirical multi‐parameter model and an artificial neural network with particular emphasis on thermal effects such as battery internal heating. The model is fast and can accurately describe constant current charging and discharging of a battery cell at a variety of ambient temperatures. Comparison to a commonly used linear kilowatt‐hour counter battery model indicates that a linear model overestimates the usable capacity of a battery at low temperatures. We highlight the importance of including internal heating in a battery model at low temperatures, as more capacity is available when internal heating is taken into account. Copyright © 2016 John Wiley & Sons, Ltd.     

Two‐layer online state‐of‐charge estimation of lithium‐ion battery with current sensor bias correction

Because of the harsh working condition in electrified vehicles, the measured current and voltage signals typically contain non‐ignorable noises and bias, which potentially decline the accuracy of state‐of‐charge estimation. In this regard, the noise and bias corruption should be well addressed to maintain sufficient accuracy and robustness. This paper improves the existing methods in the literature from two aspects: (a) A novel offset‐free equivalent circuit model is developed to remove the current bias; and (b) based on the offset‐free equivalent circuit model, a two‐layer estimator is proposed to estimate the state of charge using real‐time identified model parameters. The robustness of the two‐layer estimator against model uncertainties and the aging effect is further evaluated. Simulation and experimental results show that the proposed two‐layer estimator can effectively attenuate the current bias and estimate the state of charge accurately with the error confined to ±4% under different levels of current bias and model uncertainties.     

Using high‐HFP‐content cathode binder for mitigation of heat generation of lithium‐ion battery

We investigate the effects of thermally sensitive binder (TSB) on the temperature increase of lithium‐ion battery (LIB) coin cell subjected to severe mechanical abuse. The TSB is poly(vinylidenefluoride‐co‐hexafluoropropylene) (PVDF‐HFP), similar to conventional poly(vinylidenefluoride) (PVDF) binder but with a significant hexafluoropropylene (HFP) content. The testing data show that by using TSB, the peak temperature increase of nail‐penetrated LIB coin cell can be reduced by 20% to 40%, attributed to the softening of TSB that begins from ~80°C. The cycling performance of the LIB cells is also characterized. This research sheds light on the development of thermal‐runaway mitigation techniques.     

An enhanced temperature-dependent model and state-of-charge estimation for a Li-Ion battery using extended Kalman filter

Development of high-fidelity mathematical models and state-of-charge (SOC) estimation of Li-ion battery becomes a significant challenge when the temperature effects are considered. In this paper, we propose an enhanced temperature-dependent equivalent circuit model for a Li-ion battery and applied it for battery parameters estimation and model validation, as well as SOC estimation. First, the new battery model is elaborated, including a newly integrated resistance-capacitor structure, a static hysteresis voltage and a temperature compensation voltage term. The forgetting factor least square approach is utilized to realize the parameter identification. Next, the proposed battery model is employed to estimate battery SOC by incorporating the extended Kalman filter algorithm. Finally, simulation results are provided to demonstrate the superior performance of the proposed battery model in comparison with the common first-order Thevenin temperature model. Compared with Thevenin model, the maximal values of relative reconstruction error and root mean squared error with the proposed battery model are decreased by about 33.3% and 50.0%, respectively, for the battery terminal output voltage, 50.0% and 53.0%, respectively, for the SOC estimation, under three different test profiles.     

Numerical simulation of lithium‐ion battery performance considering electrode microstructure

A spatially resolved three‐dimensional microscale model of a lithium‐ion battery half‐cell is developed and applied to periodic electrode microstructures made up of spherical particles following a bidisperse particle size distribution. The geometries of the periodic unit cells are derived from discrete element simulations using periodic boundary conditions. Three different particle arrangements, which consist of two layered structures and one mixed particle array, as well as three different compression rates, are considered. In the study, the cathode is assumed to consist of LiMn₂O₄ as active material. Layered particle arrangements comprising the particle fraction of the smaller particle size in the region close to the separator are found to be beneficial especially for high‐rate applications. According to the simulation results, the high‐rate capability is reduced upon compression of the electrode microstructures. Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of electrode physical and chemical properties on lithium‐ion battery performance

The effect of physical and chemical properties on the performance of both positive and negative electrodes is studied for lithium‐ion (Li‐ion) batteries. These properties include the lithium diffusivity in the active electrode material, the electrical conductivity of the electrode, and the reaction rate constant at electrode active sites. The specific energy and power of the cells are determined at various discharge rates for electrodes with different properties. In addition, this study is conducted across various cell design cases. The results reveal that at moderate discharge rates, lithium diffusivity in the active negative‐electrode material has the highest impact on cell performance. The specific energy and power of the cell are improved ~11% by increasing the lithium diffusivity in the active negative‐electrode material by one order of magnitude. Around 4% improvement in the cell performance is achieved by increasing the reaction rate constant at the active sites of either electrodes by one order of magnitude. Copyright © 2013 John Wiley & Sons, Ltd.     

Passive thermal management of the lithium‐ion battery unit for a solar racing car

In this study, a three‐dimensional numerical model is developed to investigate the thermal and electrical characteristics of 18 650 lithium‐ion battery cells that are used in the solar racing car of Dokuz Eylül University, i.e., SOLARIS. The Newman, Tiedemann, Gu, and Kim (NTGK) battery model of ANSYS Fluent software is implemented to resolve the coupled multiphysics problem. In the analysis, only the discharging period of the battery is considered. Before going through parametric studies under variable weather conditions, time‐wise variations of the cell temperature and the battery voltage are evaluated both experimentally and numerically under two different ambient conditions of 0°C and 25°C. Comparative results revealed that reasonable predictions are achieved with the current battery model, and the difference between the predicted battery surface temperature and experimental data is less than 1°C. Following the model validation, the battery performance is numerically examined by applying the battery model to a real race procedure of SOLARIS. Phase change materials (PCMs) with different amounts and melting temperatures are implemented around the batteries, and transient analyses are conducted under real weather conditions. The current study aims to keep the battery temperature of a solar racing car above a certain limit to prevent the overcooling and maintain higher charging capacity. Implementation of PCM with a melting temperature of 26°C yields 3.15% of capacity increment, and such a performance improvement corresponds to 15.51 Wh of extra energy that can be extracted from an individual battery.     

Experimental and optimization of material synthesis process parameters for improving capacity of lithium‐ion battery

New methods for synthesis of active materials have been developed to improve capacity and cycle life performance of lithium‐ion batteries. Past studies have focused on routes of development of materials and new processes, which might not be economical for large‐scale production. In this regard, this study examines a widely employed carbothermal reduction technology for the synthesis of lithium‐iron phosphate (LiFePO₄/C) and investigates effects of process conditions during this synthesis on final battery performance. An experimental combined genetic programming approach is used to model the effects of crucial process conditions (sintering time, the carbon content, and the sintering temperature) on the discharge capacity of the assembled battery. Experiments are conducted to collect the discharge capacity data based on varying LiFePO₄/C synthesis conditions, and genetic programming is employed to develop a suitable functional relationship between them. The results show that the battery discharge capacity is controlled significantly by adjusting sintering temperature and carbon content, while the effect of sintering time is found to be insignificant. Further, the interaction effect of the sintering time and carbon content is much more obvious than that of the sintering time and the sintering temperature. The findings from the study pave the way for the optimum design of the synthesis process of LiFePO₄/C for a higher battery performance.