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.     

Effects of reciprocating liquid flow battery thermal management system on thermal characteristics and uniformity of large lithium-ion battery pack

To investigate the thermal characteristics and uniformity of a lithium-ion battery (LIB) pack, a second-order Thevenin circuit model of single LIB was modeled and validated experimentally. A battery thermal management system (BTMS) with reciprocating liquid flow was established based on the validated equivalent circuit model. The effects of the reciprocation period, battery module coolant flow rate and ambient temperature on the temperature and the temperature imbalance of batteries were studied. The results illustrate that the temperature difference can be effectively reduced by 3°C when the reciprocating period is 590 seconds. The reciprocating coolant flow rate is 11.5% and 33.3% that of the unidirectional flow BTMS for cooling and heating when same thermal effects are to be achieved. Under the same ambient temperature condition, the maximum temperature and average temperature difference can be reduced by 1.67°C and 3.77°C, respectively, at best for the battery module investigated with a reciprocating liquid-flow cooling system. The average temperature difference and heating power consumption could be reduced by 1.2°C and 14 kJ for reciprocating liquid flow heating system with period of 295 seconds when compared with unidirectional flow. As a result, the thermal characteristics and temperature uniformity can be effectively improved, and the parasitic power consumption can be significantly reduced through adoption of a reciprocating liquid flow BTMS.     

SOC estimation of lithium battery based on adaptive untracked Kalman filter

电池荷电状态（SOC）的准确估计是电池管理系统的关键问题,对电池的可靠性和安全性至关重要。由于多数情况下建立的电池模型精度不够高、电池系统的噪声统计是未知的或不准确的,这都会对锂离子电池系统的SOC估计会产生较大影响。本文采用二阶RC等效模型,可减小电池模型带来的误差;同时结合SageHusa滤波算法与无迹卡尔曼滤波（UKF）算法提出了一种新的SOC估计方法,基于噪声统计估计器的自适应无迹卡尔曼（AUKF）滤波算法,它可以对系统噪声进行实时修正以提高SOC的估算精度。并通过比较AUKF和UKF来验证SOC估计方法的准确性和有效性。实验结果表明,AUKF具有更高的SOC估计精度和自适应能力,在脉冲放电工况和动态工况下的估计精度均能保持在4.68%以内,可以有效地估计电池的SOC值。     

SOC estimation of lithium battery based online parameter identification and AEKF

SOC的准确估计对提高电池的动态性能和能量利用效率至关重要,估计过程中,模型参数不准确以及系统噪声的不确定性都会对结果产生较大影响。为减小模型参数辨识和系统噪声对SOC估计精度的影响,本文采用二阶RC等效电路模型,结合自适应扩展卡尔曼滤波算法（AEKF）进行锂电池的SOC估计。用带有遗忘因子的最小二乘法对模型参数进行在线辨识,以减小由参数辨识引起的估计误差,AEKF可以对系统和过程噪声进行修正,从而减小噪声对SOC估计的影响。最后分别用EKF和AEKF进行SOC估计并比较其误差,结果表明,AEKF联合最小二乘法参数在线辨识具有更高的精度和更好的适应性。     

An improved electrothermal-coupled model for the temperature estimation of an air-cooled battery pack

This work establishes an improved electrothermal-coupled model for the estimation of the temperature evolution in an air-cooled pack with three parallel branches and four serial cells in each branch. This model includes the influences of the cells' state of charge (SOC) and temperature on the ohmic and polarization resistances and polarization capacitance. The current distribution in the pack is considered in the model and applied to predicting the inconsistent effect of cell temperature. Moreover, the pipe network theory is used to model the airflow in the pack and the heat convection between the air and the batteries. An experiment is implemented to verify prediction precision in the electrical and thermal parameters of the pack. The results show that the electrothermal model accurately estimates the electrical and thermal performance of the air-cooled pack. The relative error of the pack terminal voltage between the prediction and the experiment is 3.22% under the conditions of a discharging rate is 1.5 C (C denotes the ratio of charging/discharging current to battery capacity), environment temperature of 37°C, and air inlet velocity of 6 m/s. Regarding the prediction error in the temperature, the root mean square errors of most batteries are no more than 0.6°C under the conditions of discharge rates of 1 C and 1.5 C and ambient temperatures of 17°C, 27°C, and 37°C.     

Electrical‐thermal behaviors of a cylindrical graphite‐NCA Li‐ion battery responding to external short circuit operation

Large amount of heat generated during an external short circuit (ESC) process may cause battery safety events. An experimental platform is established to explore the battery electrothermal characteristics during ESC faults. For 18650‐type nickel cobalt aluminum (NCA) batteries, ESC fault tests of different initial state of charge (SOC) values, different external resistances, or different ambient temperatures are carried out. The test case of a smaller external resistance is characterized by a shorter ESC duration with a faster cell temperature rise, whereas the case of a larger external resistance will last for a longer duration, discharge more electricity, and terminate in a slightly higher temperature. The tested batteries of high initial SOCs generally have higher temperature rise rates, smoother changes at the output current/voltage curves, but a smaller discharged capacity. The batteries of low initial SOCs can be overdischarged by the ESC operations. At low temperatures, say 0°C, the ESC process outputs much less electricity than the process at high temperatures, eg, 30°C. The initial low temperature has little effect on reducing the battery overheat due to ESC operations. The battery thermal behavior is of hysteresis property; analysis of heat generations reveals the subsequent increase of battery surface temperature after the completion of ESC discharge is due to the battery material abusive reaction heats. It is found from analytical and numerical analyses that there can have approximately 30°C temperature difference between the battery core and its surface during ESC operations. The interruption of ESC operation is very probably caused by the high battery core temperature, which leads to the destruction of solid‐electrolyte interface (SEI) film.     

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.     

Instantaneous estimation of internal temperature in lithium-ion battery by impedance measurement

Due to the various drawbacks of collecting temperature using embedded or patch thermocouple sensor, the internal temperature estimation is getting more and more attention in the field of lithium power battery. In this paper, the commercial 18650 LiFePO4 battery is selected to analyze the characteristic of Electrochemical Impedance Spectroscopy (EIS) from 0°C to 55°C of 0.1 to 10 000 Hz. The results reveal that there exists intrinsic relationship between the alternating current (AC) impedance phase shift and the internal temperature in the range of 10 to 100 Hz from 5 to 55°C. And the intrinsic relationship is not interfered with the State-of-Charge (SOC) and the State-of-Health (SOH). Subsequently, the relationship is described with a modified Arrhenius equation under the excitation frequency of 12, 44, and 79 Hz. Finally, a novel internal temperature estimation method is proposed by the AC impedance phase shift. The applicability and accuracy of the method are further verified via 10 temperature points. The results indicate that the estimation error is within 1°C in the common operating temperature range (15-45°C), suggesting that the proposed method can be applied to estimate battery internal temperature. Finally, the implementation system of real-time estimation for engineering application is constructed.     

SOC estimation method of power battery based on BP artificial neural network

电池剩余电量（SOC）的估算是电池管理系统中的关键技术之一,在众多估算方法中,神经网络在估算的准确性及鲁棒性上具有明显优势。庞大的数据量是获得SOC精确值的重要因素。针对以上问题,研究提出了基于BP人工神经网络的动力电池SOC估算方法,以某型号整包电池作为实验对象,通过对电池电压、电流、内阻及温度的数据采集,获得海量数据。建立电池的等效电路模型,考虑电池极化、充放电倍率及温度的影响对初始数据进行修正。基于MATLAB平台建立BP人工神经网络模型,数据修正后用于网络模型的训练,并验证了模型的可行性。将模型用于实验数据的预测,通过函数拟合实现了SOC的估算。最后,通过对比SOC的预测值与实际测量值,最终证明建立的人工神经网络模型对SOC估算的有效性。     

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 comparative study of lumped equivalent circuit models of a lithium battery for state of charge prediction

Battery modeling plays an important role in remaining range prediction and battery management system development. An accurate and realistic battery model is essential to design an efficient electric storage system. The goal of this paper is to investigate the performance of different circuit topologies for diffusion process in the equivalent circuit models (ECMs). The theory of diffusion process approximation by using resistive‐capacitor (RC) networks is explained in frequency domain. The terminal voltage predictive capabilities of the ECMs are compared and validated with test data. The numerical simulation results show that model prediction accuracy and computation burdens increase along with the number of RC pairs. The ECM with three RC networks is the best choice in terms of the balance between accuracy and complexity for ternary lithium batteries. In addition, a novel method of combining unscented Kalman filter (UKF) algorithm with initial state of charge (SOC) acceleration convergence for SOC estimation is proposed. The results of urban dynamometer driving schedule (UDDS) show that ECM with three RC networks has the best comprehensive performance on calculation cost and SOC estimation accuracy.     

Measurements and application of thermal characteristics of soft-packed NCM lithium-ion power battery

锂离子电池的极化内阻是不可逆热测试的关键参数。为了更准确地计算极化内阻,针对三元软包锂离子动力电池,进行了HPPC测试、熵热系数测试、充放电温升测试,采用两种方法对极化内阻进行了计算,一种是通过电压变化量除以电流得到,另一种是通过建立二阶RC模型,结合HPPC测试工况辨识得到。根据两种方法得到的极化内阻,结合Bernardi生热速率模型公式对电池进行了1C充电和0.5C、1C、2C放电下的温度场仿真,并与红外热成像仪记录到的温度分布进行了对比。结果表明：根据二阶RC模型得到的极化内阻进行的仿真与实验数据吻合较好,说明利用二阶RC模型得到的极化内阻更加适用于电池持续充放电过程中的热分析。模型很好地模拟了电池不同充放电倍率下的温度场信息,对电池热分析及热管理可起到指导作用。     

Second-order RC modeling and parameter identification of electric vehicle power battery

建立精确的动力电池模型是电池管理系统（battery management system,BMS）开发过程中的重要环节,电池系统具有较强的非线性特性,其模型参数随多种因素的变化而变化。在电池模型参数辨识过程中,考虑的可变因素越多,辨识结果越准确,但模型的运行速度将降低,影响其实际应用。在各种可变因素中,电池荷电状态（state of charge,SOC）对电池模型参数的影响最为显著,对不同SOC下电池模型参数进行辨识并应用于电池模型,将在提高模型精度的同时保持较好的实时性。本文以动力锂电池为对象,采用二阶RC等效电路模型,通过试验得到电池组在不同SOC下的回弹电压数据,采用最小二乘拟合法辨识不同SOC状态下的模型参数。在此基础上搭建模型参数随SOC变化的实时仿真模型,并对模型进行仿真和试验验证,结果表明模型具有较高的精度和实时性。     

Cycling degradation testing and analysis of a LiFePO4 battery at actual conditions

This paper presents a degradation testing of a lithium‐ion battery developed using real world drive cycles obtained from an electric vehicle (EV). For this, a data logger was installed in the EV, and real world drive cycle data were collected. The EV battery system consists of 3 lithium‐ion battery packs with a total of 20 battery modules in series. Each module contains 6 series by 49 parallel lithium‐ion cells. The vehicle was driven in the province of Ontario, Canada, and several drive cycles were recorded over a 3‐month period. However, only 4 drive cycles with statistical analysis are reported in this paper. The reported drive cycles consist of different modes: acceleration, constant speed, and deceleration in both highway and city driving at ?6°C, 2°C, 10°C, and 23°C ambient temperatures with all accessories on. Additionally, individual cell characterization was conducted using a C/25 (0.8A) charge‐discharge cycle and hybrid pulse power characterization (HPPC). The Thevenin battery model was constructed in MATLAB along with an empirical degradation model and validated in terms of voltage and SOC for all drive cycles reported. The presented model closely estimated the profiles observed in the experimental data. Data collected from the drive cycles showed that a 4.6% capacity fade occurred over the 3 months of driving. The empirical degradation model was fitted to these data, and an extrapolation estimated that 20% capacity fade would occur after 900 daily drive cycles.     

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.     

Preheating strategy of variable-frequency pulse for lithium battery in cold weather

Aiming to the issue of charging difficulty and capacity fading for lithium-ion battery at low temperature, this study proposes a preheating strategy using variable-frequency pulse. The innovation of this paper is to propose the thermo-electric coupling model based on the electrochemical impedance spectroscopy of battery at different temperatures, integrated with variable frequency changing for pulse method to develop an effective inner pre-heating strategy. Meanwhile, the evaluating method of impact of this strategy on capacity fading of battery has also been proposed to examine its effectiveness, to find the optimal strategy. First, temperature rise model and the thermo-electric coupling model at different temperatures according to the equivalent circuit model of battery are presented. Further, optimal heating frequency of current pulse at different temperatures is calculated according to the changing of internal impedance. The results show that the optimal variable-frequency pulse pre-heating strategy can heat the lithium-ion battery from −20°C to 5°C in 1000 seconds. Meanwhile, it brings less damage to the battery health and improves the performance of battery in cold weather based on the views of power consumption, capacity attenuation, and internal impedance changes.     

Experimental research on temperature rise and electric characteristics of aluminum air battery under open‐circuit condition for new energy vehicle

Due to lack of systematic research on open‐circuit voltage (OCV) and electrolyte temperature rise characteristics of aluminum air battery, in order to explore the influential factors on the OCV and electrolyte temperature rise of aluminum air battery, in this paper, for the first time, we studied the effects of different ambient temperature conditions, different concentrations of NaOH and KOH electrolyte, and pure aluminum and aluminum alloy on the OCV and electrolyte temperature rise of aluminum air battery. Results show that the OCV of aluminum air battery is obviously affected by ambient temperature conditions, electrolyte concentration, and different anode materials. The OCV range is 1.5 to 1.8 V at 0°C under different KOH‐electrolyte concentrations when aluminum alloy is used as anode material; with the increase of ambient temperature, the OCV will rise, and the range is 1.8 to 1.95 V. The working process of aluminum air battery is accompanied by the phenomenon of heat release, and the temperature rise range of electrolyte will not exceed 7°C when aluminum alloy is used as the anode material; however, the highest temperature of the electrolyte can reach 100°C when pure aluminum is used as the negative electrode material. The results of this study will provide theoretical guidance for designing aluminum air batteries and identifying their optimal operating conditions.     

Effect of high Ni on battery thermal safety

Frequent accidents involving Li-ion batteries have prompted higher safety requirements for these batteries. In this study, the high-temperature, thermal runaway (TR) characteristic parameters at 100% state of charge (SOC) for cylindrical NCM811 batteries with a high-energy density were compared to the widely commercialized NCM523 batteries. The average TR trigger temperature of NCM811 battery was 157.54°C, which was 20.62°C lower than that of NCM523. Moreover, the average TR maximum temperature of NCM811 battery is 858.22°C, which was 212.81°C higher than that of NCM523. The maximum TR temperature of the NCM811 battery was 1289.53°C. The high Ni batteries exhibited poor thermal stability and severe TR. An increase in the Ni content resulted in increased fluctuations in the battery's internal TR reaction because high Ni batteries have a poor TR consistency and are difficult to accurately control. The TR combustion explosion of the fully charged NCM811 battery lasted for approximately 1.36 seconds. The combustion explosion severely damaged the positive electrode, and there was a collapse of the negative layered structure. The Cu current collector surface melted locally owing to the high temperature. Moreover, Ni, Co, and Mn particles appeared in the Cu current collectors and graphite.     

Equivalent circuit model parameters of a high-power Li-ion battery: Thermal and state of charge effects

Equivalent circuit model (EMC) of a high-power Li-ion battery that accounts for both temperature and state of charge (SOC) effects known to influence battery performance is presented. Electrochemical impedance measurements of a commercial high power Li-ion battery obtained in the temperature range 20 to 50 °C at various SOC values was used to develop a simple EMC which was used in combination with a non-linear least squares fitting procedure that used thirteen parameters for the analysis of the Li-ion cell. The experimental results show that the solution and charge transfer resistances decreased with increase in cell operating temperature and decreasing SOC. On the other hand, the Warburg admittance increased with increasing temperature and decreasing SOC. The developed model correlations that are capable of being used in process control algorithms are presented for the observed impedance behavior with respect to temperature and SOC effects. The predicted model parameters for the impedance elements R_s, R_ct and Y₀₁₃ show low variance of 5% when compared to the experimental data and therefore indicates a good statistical agreement of correlation model to the actual experimental values.     

工作温度对磷酸铁锂电池SOC影响及研究进展

储能电池在新能源并网、新能源汽车等产业领域发挥着重要作用,为了对电池进行有效地控制与管理,需要配备必要的电池管理系统,电池荷电状态（SOC）是其中最为重要的一环。磷酸铁锂（LiFePO4,LFP）电池SOC与多个影响因素密切相关,呈强非线性,本文重点归纳温度对磷酸铁锂电池SOC的影响。首先将工作温度对开路电压、实际容量、充放电效率、自放电率及电池老化等电池特性的影响进行归纳总结,随后通过对工作温度的影响规律进行分析、总结和归纳,基于经典“开路电压 + 安时积分”法将温度参数直接或间接引入到SOC的实时估算模型中,得到考虑温度参数的新模型,进而提高电池SOC的估算精度。