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 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 of lithium‐ion batteries for electric vehicles

Thermal issues associated with electric vehicle battery packs can significantly affect performance and life cycle. Fundamental heat transfer principles and performance characteristics of commercial lithium‐ion battery are used to predict the temperature distributions in a typical battery pack under a range of discharge conditions. Various cooling strategies are implemented to examine the relationship between battery thermal behavior and design parameters. By studying the effect of cooling conditions and pack configuration on battery temperature, information is obtained as to how to maintain operating temperature by designing proper battery configuration and choosing proper cooling systems. It was found that a cooling strategy based on distributed forced convection is an efficient, cost‐effective method which can provide uniform temperature and voltage distributions within the battery pack at various discharge rates. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

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.     

Low‐temperature reversible capacity loss and aging mechanism in lithium‐ion batteries for different discharge profiles

In this paper, reversible capacity loss of lithium‐ion batteries that cycled with different discharge profiles (0.5, 1, and 2 C) is investigated at low temperature (?10°C). The results show that the capacity and power degradation is more severe under the condition of low discharge rate, not the widely accepted high discharge rate. To shed some light on the aging phenomena, noninvasive electrochemical methods, ie, incremental capacity and differential voltage analysis, are applied to identify and quantify the effects of different degradation modes (DMs). Apart from the resistance increase, the DMs include the loss of lithium inventory (LLI) and the loss of active material (LAM). Both LLI and LAM decay to a greater extent for the cell cycled with lower discharge rate, and the growth of LAM is higher than that of LLI. Further, the analysis of state of charge (SOC) window shows that the earlier cutoff of the high discharge rate can lead to less mechanical and thermal stress on cathode materials, thus a lower degradation rate. Another cause is that the lithium plating on the anode materials can be mitigated by increasing the charging temperature which results from preceding high rate discharging.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

A novel multiobjective charging optimization method of power lithium‐ion batteries based on charging time and temperature rise

Power lithium‐ion batteries have been widely utilized in energy storage system and electric vehicles, because these batteries are characterized by high energy density and power density, long cycle life, and low self‐discharge rate. However, battery charging always takes a long time, and the high current rate inevitably causes great temperature rises, which is the bottleneck for practical applications. This paper presents a multiobjective charging optimization strategy for power lithium‐ion battery multistage charging. The Pareto front is obtained using multiobjective particle swarm optimization (MOPSO) method, and the optimal solution is selected using technique for order of preference by similarity to ideal solution (TOPSIS) method. This strategy aims to achieve fast charging with a relatively low temperature rise. The MOPSO algorithm searches the potential feasible solutions that satisfy two objectives, and the TOPSIS method determines the optimal solution. The one‐order resistor‐capacitor (RC) equivalent circuit model is utilized to describe the model parameter variation with different current rates and state of charges (SOCs) as well as temperature rises during charging. And battery temperature variations are estimated using thermal model. Then a PSO‐based multiobjective optimization method for power lithium‐ion battery multistage charging is proposed to balance charging speed and temperature rise, and the best charging stage currents are obtained using the TOPSIS method. Finally, the optimal results are experimentally verified with a power lithium‐ion battery, and fast charging is achieved within 1534 s with a 4.1°C temperature rise.     

Computational study about the effect of electrode morphology on the performance of lithium‐ion batteries

Electrode morphology has significant influence on the performance of lithium‐ion batteries in that it controls electrical conductivity and electrode utilization by establishing electrical connectivity in the electrode. The present study investigates the effect of the electrode morphology on battery performance by combining two different mathematical models. First, a two‐dimensional, direct numerical simulation (DNS) model is introduced, which stochastically generates electrode morphology and calculates electrical conduction and electrode utilization. Various simulations are conducted to evaluate the effect of the active particle coating, conductive agent loading, particle size, and electrode compression by using the DNS model. Second, data acquired from the DNS model are applied to the blended‐electrode model to evaluate battery performance. Calculation result confirms that electrode morphologies have significant effects on both capacity and power of lithium‐ion batteries. Copyright © 2016 John Wiley & Sons, Ltd.     

A validation study of lithium‐ion cell constant c‐rate discharge simulation with Battery Design Studio®

We compare battery performance simulations from a commercial lithium‐ion battery modeling software package against manufacturer performance specifications and laboratory tests to assess model validity. A set of commercially manufactured spiral wound lithium‐ion cells were electrochemically tested and then disassembled and physically characterized. The Battery Design Studio® (BDS) software was then used to create a mathematical model of each battery, and discharge simulations at constant C‐rates ranging from C/5 to 2C were compared against laboratory tests and manufacturer performance specifications. Results indicate that BDS predictions of total energy delivered under our constant C‐rate battery discharge tests are within 6.5% of laboratory measurements for a full discharge and within 2.8% when a 60% state of charge window is considered. Average discrepancy is substantially lower. In all cases, the discrepancy in simulated vs. manufacturer specifications or laboratory results of energy and capacity delivered was comparable to the discrepancy between manufacturer specifications and laboratory results. Results suggest that BDS can provide sufficient accuracy in discharge performance simulations for many applications. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

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.     

Introducing the energy efficiency map of lithium‐ion batteries

The charge, discharge, and total energy efficiencies of lithium‐ion batteries (LIBs) are formulated based on the irreversible heat generated in LIBs, and the basics of the energy efficiency map of these batteries are established. This map consists of several constant energy efficiency curves in a graph, where the x‐axis is the battery capacity and the y‐axis is the battery charge/discharge rate (C‐rate). In order to introduce the energy efficiency map, the efficiency maps of typical LIB families with graphite/LiCoO₂, graphite/LiFePO₄, and graphite/LiMn₂O₄ anode/cathode are generated and illustrated in this paper. The methods of usage and applications of the developed efficiency map are also described. To show the application of the efficiency map, the effects of fast charging, nominal capacity, and chemistry of typical LIB families on their energy efficiency are studied using the generated maps. It is shown how energy saving can be achieved via energy efficiency maps. Overall, the energy efficiency map is introduced as a useful tool for engineers and researchers to choose LIBs with higher energy efficiency for any targeted applications. The developed map can be also used by energy systems designers to obtain accurate efficiency of LIBs when they incorporate these batteries into their energy systems.