Model‐based unscented Kalman filter observer design for lithium‐ion battery state of charge estimation

Accurate battery state‐of‐charge is essential for both driver notification and battery management units reliability in electric vehicle/hybrid electric vehicle. It is necessary to develop a robust state of charge (SOC) estimation approach to cope with nonlinear dynamic battery systems. This paper proposed an estimation method to identify the SOC online based on equivalent circuit battery model and unscented Kalman filter technique. Firstly, the parameters of dynamic battery model are identified offline and validated through typical electric vehicle road operation to guarantee its precision. Then the performance with respect to converge time, observer accuracy, robustness against system modeling errors, and mismatched initial SOC guess values is investigated. The accuracy of proposed estimation algorithm is validated under improved hybrid power pulse characterization test and New European Driving Cycle. Experiment and numerical simulation results clearly demonstrate that the proposed method is highly reliable with good robustness to different operating conditions and battery aging.     

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.     

The equivalent circuit battery model parameter sensitivity analysis for lithium‐ion batteries by Monte Carlo simulation

To enhance the estimation accuracy of battery's state of charge, it is imperative to estimate the battery model parameter. To reduce the calculation efforts, the number of the battery model parameter to be estimated should be less while ensuring the state of charge estimation accuracy. Especially in engineering applications, the calculating ability is usually limited. So, it needs to choose the critical battery model parameter to be estimated. This paper's contributions are as follows: The global sensitivity analysis of the battery model parameter is achieved by the Monte Carlo simulation method. The results show that the open circuit voltage and the ohmic resistance are the high sensitivity parameters. Guided by the results of parameter sensitivity analysis, a dual extended Kalman filters method is utilized to achieve online battery model parameter estimation. The experiments prove that the state of charge estimation accuracy is improved by the online parameter estimation. Estimating high sensitivity parameters can reduce running time. And the SOC estimation accuracy can be guaranteed.     

Li‐ion battery dynamics model parameter estimation using datasheets and particle swarm optimization

Dynamics modeling is of fundamental importance to Li‐ion battery design and manufacturing. Accurate dynamics models established can be used to optimize the operation strategy, manage the life cycle, and thus ensure the economic and safe operation of the batteries. The Li‐ion dynamics model examined in this paper has integrated both empirical and electrochemical aspects, and it has been specifically validated for electric vehicle applications using experimental data. Previously, the model parameter estimation was done by manually picking three key points from the discharge curve obtained from the datasheet. The approach is quite subjective and error prone. The resulted model may deviate greatly from the experimental curve. To address this issue, this paper proposes to use particle swarm optimization to more objectively estimate the model parameters. Results from case studies show that the proposed approach provides more accurate estimation of the true parameters, and thus the new approach can more precisely capture the battery dynamics. In addition, this approach is generic because it is independent of specific battery chemistries and applicable to many different types of Li‐ion batteries. Copyright © 2016 John Wiley & Sons, Ltd.     

Study on electrochemical and thermal characteristics of lithium‐ion battery using the electrochemical‐thermal coupled model

The higher specific energy leads to more heat generation of a battery, which affects the performance and cycle life of a battery and even results in some security problems. In this paper, the capacity calibration, Hybrid Pulse Power Characteristic (HPPC), constant current (dis)charging, and entropy heat coefficient tests of chosen 11‐Ah lithium‐ion batteries are carried out. The entropy heat coefficient increases firstly and then decreases with the increase of the depth of discharge (DOD) and reaches the maximum value near 50% DOD. An electrochemical‐thermal coupled model of the chosen battery is established and then verified by the tests. The simulation voltage and temperature trends are in agreement with the test results. The maximum voltage and temperature error is within 2.06% and 0.4°C, respectively. Based on the established model, the effects of adjustable parameters on electrochemical characteristic are systematically studied. Results show that the average current density, the thickness of the positive electrode, the initial and maximum lithium concentration of the positive electrode, and the radius of the positive electrode particle have great influence on battery capacity and voltage. In addition, the influence degree of the internal resistance of the solid electrolyte interface (SEI) layer, the thickness of negative electrode, and the initial and maximum lithium concentration of the negative electrode on the capacity and voltage is associated with certain constraints. Meanwhile, the influences of adjustable parameters related to thermal characteristic are also systematically analyzed. Results show that the average current density, the convective heat transfer coefficient, the thickness, and the maximum lithium concentration of the positive electrode have great influence on the temperature rise. Besides, the uniformity of the temperature distribution deteriorates with the increase of the convective heat transfer coefficient.     

Correlating uncertainties of a lithium‐ion battery – A Monte Carlo simulation

Safety issues raised from a lithium‐ion battery during operation can be attributed to the variation of its temperature, which is, in turn, associated with the uncertainties in the parameters such as material properties and operating conditions. In this study, a Monte Carlo simulation of a mechanistic lithium‐ion battery model is conducted to capture the probabilistic nature of uncertainties in the parameters and their relative importance to the temperature of a lithium‐ion battery cell. Sensitivity analysis is statistically performed, and the varied parameters are ranked according to their contributions to the variation of the battery temperature. Statistical analysis is also conducted on the distribution of the temperature and deviation from its normality has been identified. These analyses can provide valuable information for manufactures in the area of resource partitioning for quality and safety control. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Subspace‐based modeling and parameter identification of lithium‐ion batteries

For reliable and safe operation of lithium‐ion batteries in electric vehicles, the monitoring of state‐of‐charge and state‐of‐health is necessary. However, these internal states cannot be measured directly, which are usually estimated through model‐based techniques. Therefore, an accurate application‐oriented battery model is of significant importance. The purpose of this paper is to present a novel method on battery modeling and parameter identification. In this work, a state‐space model with clear mathematical and electrochemical meanings is proposed on the basis of the electrochemical basics of lithium‐ion batteries. The frequency‐domain characteristics of the lithium‐ion batteries are also investigated. On the basis of the frequency analysis, an identification test profile that can excite the dynamic characteristics of the battery fully and persistently is proposed. A subspace‐based algorithm is then adopted to identify the parameters of the battery model. The performance and robustness of the estimated model are validated through some experiments and simulations. The validation results show that the proposed method can achieve an acceptable accuracy with the maximum error being less than 2%. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

The indentation analysis triggering internal short circuit of lithium‐ion pouch battery based on shape function theory

A novel indentation theory with homogenized, isotropic, and continuum model based on different shape functions is investigated to predict the mechanical behavior triggering internal short circuit of lithium‐ion pouch battery (LIPB) under indentation loading. By taking energy conservation principle into account, the relationship among indentation force, indentation displacement, and indentation region of LIPB is proposed. The results conclude that the effects of deformation region and indentation displacement play an important role in mechanical behavior triggering internal short circuit. The theoretical results based on sine, cosine, and quadratic shape functions agree well with experimental results. Both of increasing compressed yield stress of jellyroll core and punch radius and decreasing flow stress of soft casing and thickness of soft casing can avoid triggering internal short circuit of LIPB. According to current research, the indentation loading is reduced to flat compression when punch radius approaches infinity, and the internal short circuit of LIPB under flat compression is very difficult to be triggered. Effectiveness and application scope of different shape functions are also discussed. The theoretical model provides guidance for improving mechanical behavior, decreasing internal short circuit, and optimizing structure of LIPB in industrial manufacture.     

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.     

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.     

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.     

Thermal analysis of high‐power lithium‐ion battery packs using flow network approach

High‐power applications of lithium‐ion batteries require efficient thermal management systems. In this work, a lumped capacitance heat transfer model is developed in conjunction with a flow network approach to study performance of a commercial‐size lithium‐ion battery pack, under various design and operating conditions of a thermal management system. In order to assess the battery thermal management system, capabilities of air, silicone oil, and water are examined as three potential coolant fluids. Different flow configurations are considered, and temperature dispersions, cell‐averaged voltage distributions, and parasitic losses due to the fan/pump power demand are calculated. It is found that application of a coolant with an appropriate viscosity and heat capacity, such as water, in conjunction with a flow configuration with more than one inlet will result in uniform temperature and voltage distributions in the battery pack while keeping the power requirement at low, acceptable levels. Simulation results are presented and compared with literature for model validation and to show the superior capability of the proposed battery pack design methodology. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

A new state‐of‐charge estimation method for electric vehicle lithium‐ion batteries based on multiple input parameter fitting model

The estimation of state‐of‐charge (SOC) is crucial to determine the remaining capacity of the Lithium‐Ion battery, and thus plays an important role in many electric vehicle control and energy storage management problems. The accuracy of the estimated SOC depends mostly on the accuracy of the battery model, which is mainly affected by factors like temperature, State of Health (SOH), and chemical reactions. Also many characteristic parameters of the battery cell, such as the output voltage, the internal resistance and so on, have close relations with SOC. Battery models are often identified by a large amount of experiments under different SOCs and temperatures. To resolve this difficulty and also improve modeling accuracy, a multiple input parameter fitting model of the Lithium‐Ion battery and the factors that would affect the accuracy of the battery model are derived from the Nernst equation in this paper. Statistics theory is applied to obtain a more accurate battery model while using less measurement data. The relevant parameters can be calculated by data fitting through measurement on factors like continuously changing temperatures. From the obtained battery model, Extended Kalman Filter algorithm is applied to estimate the SOC. Finally, simulation and experimental results are given to illustrate the advantage of the proposed SOC estimation method. It is found that the proposed SOC estimation method always satisfies the precision requirement in the relevant Standards under different environmental temperatures. Particularly, the SOC estimation accuracy can be improved by 14% under low temperatures below 0 °C compared with existing methods. Copyright © 2017 John Wiley & Sons, Ltd.     

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.