State-of-health monitoring of lithium-ion batteries in electric vehicles by on-board internal resistance estimation

For reliable and safe operation of lithium-ion batteries in electric or hybrid vehicles, diagnosis of the cell degradation is necessary. This can be achieved by monitoring the increase of the internal resistance of the battery cells over the whole lifetime of the battery. In this paper, a method to identify the internal resistance in a hybrid vehicle is presented. Therefore, a special purpose model deduced from an equivalent circuit is developed. This model contains parameters depending on the degradation of the battery cell. To achieve the required robustness and stable results under these conditions, the method uses specific signal intervals occurring during normal operation of the battery in a hybrid vehicle. This identification signal has a defined timespan and occurs regularly. The identification is done on vehicle measurement data of terminal cell voltage and current collected with a usual vehicle sampling rate. Using the adapted internal resistance value in the model, a degradation index is calculated by compensating other influences, e.g. battery temperature. This task is the main challenge, as the impact of the temperature on the resistance, for example, is one order of magnitude higher than the influence of the degradation for the investigated lithium-ion cell. The developed estimation and monitoring method is validated with measurement data from single cells and shows good results and very low computational effort.     

Research on parameter identification and state of charge estimation of improved equivalent circuit model of Li-ion battery based on temperature effects for battery thermal management

The performance and parameters of Li-ion battery are greatly affected by temperature. As a significant battery parameter, state of charge (SOC) is affected by temperature during the estimation process. In this paper, an improved equivalent circuit model (IECM) considering the influence of ambient temperatures and battery surface temperature (BST) on battery parameters based on second-order RC model have been proposed. The exponential function fitting (EFF) method was used to identify battery model parameters at 5 ambient temperatures including −10°C, 0°C, 10°C, 25°C and 40°C, fitting the relationship between internal resistance and BST. Then, the SOC of the IECM was estimated based on the extended Kalman filter (EKF) algorithm. Using the result calculated by the Ampere-hour integration method as the standard, the data of battery under open circuit voltage (OCV) test profile and dynamic stress test (DST) profile at different ambient temperatures has been compared with the ordinary second-order RC model, and the advantages of the SOC estimation accuracy with IECM was verified. The numerical results showed that the IECM can improve the estimation accuracy of battery SOC under different operating conditions.     

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.     

Rapid test and non-linear model characterisation of solid-state lithium-ion batteries

This paper describes a rapid test-procedure that can be used to derive parameters of a proposed battery model. The battery model is a non-linear dynamic equivalent circuit model, which is based on Randle’s model for electrochemical impedance [J. Power Sources 54 (1995) 393]. The level of sophistication has been selected such that it gives a satisfactory prediction of battery performance, but simple enough to enable on-line identification and adaptation of model parameters based on measurements of terminal voltage, current and temperature during usage. The paper also presents test data for a commercial 100 Ah battery including ageing effects.     

Equivalent electrical model for a proton exchange membrane (PEM) electrolyser

In this work, an electrical equivalent model for a proton exchange membrane (PEM) electrolyser has been developed. Through experimental analysis, the input current–voltage (I–V) characteristic for a single PEM electrolyser cell has been modelled under steady-state conditions. It has been developed by using electrical equivalent circuit topology in which the useful power conversion and losses have been taken into account. Electrolytic hydrogen production rates of PEM electrolyser cell have been calculated with respect to the input current and power. The developed model has been tested with experiments results at the nominal operating temperature. The experimental results have been verified with the developed model results and the relative errors between them are around 1–2%. It has been observed that the electrolytic hydrogen production rate increases with the input current in a linear fashion. But the variation of electrolytic hydrogen production rate with the input electrical power is non-linear (i.e. logarithmic). These characteristics are verified by using the developed electrical equivalent model of PEM electrolyser cell. The parameters of the developed model can also be defined by taking into account of temperature and pressure effects. The equivalent electrical model of PEM electrolyser is very useful for analysing the electrical energy system behaviour in which the energy is stored in the form of electrolytic hydrogen.     

基于有源纹波补偿器级联多电平电池储能系统设计

通过分析传统的H桥直流端电流的谐波特性,针对其截止频率较低、影响变换器的有功响应速率、产生很大的恒定磁通、设备的体积较大的问题,提出一种有源纹波补偿器,通过匹配适当容量的开关器件,使得ARC电路在无直流源的前提下,通过单闭环单参数的控制实现电池纹波电流抑制,优化提升了LC无源滤波的效果。仿真结果表明,含有ARC电路的级联多电平储能变换器在电网不平衡工况下可以正常工作,同时流入电池的纹波电流得到了有效抑制。该研究成果应用于电池储能系统,可提供稳定的频率和电压支撑,实现经济运行,可有效解决电动汽车充电的随机性和波动性所带来的电能质量问题。     

Intelligent optimization methodology of battery pack for electric vehicles: A multidisciplinary perspective

Past studies focused on proposing new materials for batteries components, state of health (SOH) prediction, thermal design, equivalent circuit modeling, and so on. Those studies have been implemented on individual basis on a single battery or battery pack. However, there is hardly any research found that encompasses all the multidisciplinary aspects (such as materials, SOH, intelligent configuration [assembly], thermal design, mechanical safety, and recycling of materials and pack) simultaneously for the battery pack design of electric vehicles. This research article proposes a synthetic methodology for an advanced design of battery pack and its components by incorporating optimal scenario of materials selection for battery electrodes, SOH estimation, configurations (assembly) of cells, thermal (air and liquid cooling) design, battery pack casing mechanical safety, and recycling aspects of battery and battery pack. The problem is divided into the several parts and methodology for each is proposed. Cumulative advantages of the methodology with six future critical directions are discussed in the end.     

Transient-boundary voltage method for measurement of equivalent circuit components of rechargeable batteries

A method is presented for measuring the equivalent circuit components of rechargeable batteries. The temporal discharge-rest-charge-rest sequence of a rechargeable battery is described, using the principles of transient circuit analysis, to derive equations for the battery voltage as a function of time during voltage transients and at the boundaries at transitions between transient phases. The equations lead to a new measurement method for battery characterization. The equivalent circuit of the battery is described as an ideal voltage source in series with a resistor and the parallel combination of a resistor and a capacitor. The battery model uses different values of resistance and capacitance, in the parallel combination, during the different phases of the discharge-rest-charge-rest sequence. The method is used to measure the circuit parameters of a nickel-cadmium battery.     

基于开路电压回升速率和交流阻抗相结合的一种锂离子电池SOH算法

本研究所述SOH（State-of-health）估算方法是通过记录锂离子动力电池放电截止之后的开路电压值的变化,从而得出开路电压回升速率,作为主要因素判断值;对锂离子动力电池进行交流阻抗测试,得出交流阻抗图谱,并进行拟合,从而计算出锂离子动力电池的内部阻抗值,作为次要因素判断值,将主要因素判断值和次要因素判断值相加即为锂离子动力电池的SOH值,使得计算结果更加准确。该方法中考虑了电池温度、放电电流、放电截止电压等因素,得到锂离子动力电池开路电压回升曲线及内部各部分阻值。比较研究表明：该方法能够简便、快速地估算出锂离子动力电池的健康状态。     

Extracting equivalent circuit parameters of lead–acid cells from sparse impedance measurements

A method for extracting the equivalent circuit parameters of a lead–acid battery from sparse (only three) impedance spectroscopy observations at three different frequencies is outlined. The method is ideal for finding the parameters in an equivalent circuit consisting of bulk resistance, a reaction resistance and a constant phase element (CPE). Electrochemical impedance spectroscopy (EIS) measurements were made on spirally wound 2.5 Ah lead–acid cells. The equivalent circuit parameters found using our method closely compare with those extracted from the EIS measurements. The complete EIS spectrum calculated using the estimated circuit parameters at all other frequencies also closely matched the actual measurements.     

Equivalent circuit components of nickel-metal hydride battery at different states of charge

Equations that describe the voltage variations with time of rechargeable batteries during charging and discharging were used to determine the component values of the equivalent circuit of nickel-metal hydride batteries under different states of charge (SOC). The equivalent circuit of the battery was described as an ideal voltage source in series with a resistor and the parallel combination of a resistor and a capacitor. The battery model used different values of resistance and capacitance, in the parallel combination, during the different phases of the discharge-rest-charge-rest sequence. The results show that the resistances in the equivalent circuit are approximately constant with variations in the SOC. For the discharge and charge phases the capacitor value increased and decreased, respectively, as the SOC decreased. The value of the capacitor in the parallel RC circuit is an indicator of the battery SOC.     

Thermal analysis of a Li‐ion battery module under realistic EV operating conditions

The thermal behavior of a Li‐ion battery module that belongs to the battery system of an actual electric vehicle prototype was numerically investigated. Realistic driving loads and passive cooling conditions were considered. A combination of a vehicle dynamics model, an equivalent electric circuit battery model, and a 3D finite‐element thermal model was used in the analysis. Temperature and electric potential measurements, performed at the cell and module levels, were first used for model calibration. Electric currents, associated with the ARTEMIS driving cycles, were then calculated and applied in the battery model to predict the heat sources for the thermal model. It was found that the temperature increase corresponding to urban transportation requirements in European countries is tolerable. Nevertheless, road and highway applications would result in a temperature increase that accelerates cell ageing, and an active cooling strategy is required. Copyright © 2012 John Wiley & Sons, Ltd.     

A circuit approach to finite element analysis of a double squirrelcage induction motor

A method for analyzing the losses and the torque of an induction motor with a double cage rotor is presented. The tentative values for the currents for the analysis are found using an analytical procedure. The parameters of an equivalent circuit are then calculated by means of a finite-element method. The actual current distribution in the rotor bars, including the eddy current distribution, results from the finite-element solution. New current estimates are found from the obtained circuit and are used to establish a corrected field distribution. Using the losses due to eddy currents, the equivalent resistance of the rotor may be calculated, and using the rotor losses, the torques are calculated. Assuming linearity, the complex power yields the inductances. The resulting equivalent circuit can then yield a better estimate for the current. This constitutes an iterative procedure which can be continued to any desired convergence accuracy for the currents     

Performance simulation of current/voltage-characteristics for SOFC single cell by means of detailed impedance analysis

We present a zero dimensional stationary model which precisely predicts the current-voltage-characteristics of anode supported SOFC single cells over a wide range of operating conditions. The different kinds of electrode polarization resistances are separated from experimental impedance data by means of a detailed equivalent circuit model developed specifically for the analyzed cell type. The activation losses are modeled by the Butler-Volmer equation, whereas the loss contributions from gas diffusion polarizations are calculated from Fick's law. The partial pressure and temperature dependency of the cathodic and anodic exchange current density could be determined by a fit of semi empirical power law model equations. The exponents c and d for the CO and CO₂ partial pressure dependency of the anodic exchange current density are determined independently of each other. This paper presents the modeling results for a wide range of operation parameters as well as their experimental verification.     

大级差电源密集型电网短路电流直流分量对断路器的影响

西北电网电压级差大且电源密集易导致系统短路电流超标,常采用串联电抗器、高阻抗变压器等限流措施,但却增大了系统电抗,使短路电流直流分量衰减变慢,可能导致断路器开断失败。以新疆电网乌北区域为研究对象,基于PSASP短路模块的计算结果对大型电网进行等值简化,并在EMTP/ATP中重构简化后的等值网络。校验了EMTP/ATP的等值网络与原网络的短路电流交流分量基本一致,在此基础上定量计算短路电流直流分量对断路器的影响,若仍以短路电流交流分量校验断路器开断能力,则断路器需要留有一定的裕度。     

Equivalent circuit components of nickel-cadmium battery at different states of charge

Equations that describe the voltage variations with time of a rechargeable battery during charging and discharging were used to determine the component values of the equivalent circuit of nickel-cadmium batteries under different states of charge (SOC). The equivalent circuit of the battery was described as an ideal voltage source in series with a resistor and the parallel combination of a resistor and a capacitor. The battery model used different values of resistance and capacitance, in the parallel combination, during the different phases of the discharge-rest-charge-rest sequence. The results show that the series resistance is approximately constant with variations in the SOC while the resistor in the parallel RC circuit increases as the SOC decreases. For the discharge and charge phases the capacitor value increased and decreased, respectively, as the SOC decreased. The value of the resistor or capacitor in the parallel RC circuit is an indicator of the battery SOC.     

RC equivalent circuit model of lumped parameters for lithium ion batteries in electric vehicles

本项目以纯电动汽车锂离子动力电池集总参数RC等效电路模型为研究对象,在传统模型基础上,考虑了电池的极化效应特性和迟滞电压特性,创建一种新的锂离子动力电池动态等效电路模型;基于实验测试,对该模型参数进行了辨识,并通过实验分析验证,该模型的估算误差为2%,比传统一阶及二阶模型准确,比三阶RC模型简单。     

Evaluation of uncertainty of lithium battery capacity measurement and equivalent model validation method

锂电池容量是评估电池健康状态的主要参数，但由于电池容量溯源体系还没有建立，无法明确容量测量精度。本文在理解电池充放电原理的基础上，建立电池容量测量不确定度模型，定量分析影响电池容量测量的因素，提出基于不确定度分析优化锂电池等效电路模型的修正方法，通过实际测量的充电工作电压、容量与模型计算的电压、容量相比较，判断模型计算值是否在实际测量值的不确定度结果范围内，尽量避免由于实际测量偏差造成的模型可靠性的降低。     

Electro-thermal battery model identification for automotive applications

This paper describes a model identification procedure for identifying an electro-thermal model of lithium ion batteries used in automotive applications. The dynamic model structure adopted is based on an equivalent circuit model whose parameters are scheduled on the state-of-charge, temperature, and current direction. Linear spline functions are used as the functional form for the parametric dependence. The model identified in this way is valid inside a large range of temperatures and state-of-charge, so that the resulting model can be used for automotive applications such as on-board estimation of the state-of-charge and state-of-health. The model coefficients are identified using a multiple step genetic algorithm based optimization procedure designed for large scale optimization problems. The validity of the procedure is demonstrated experimentally for an A123 lithium ion iron-phosphate battery.