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.     

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.     

Characterization of high-power lithium-ion batteries by electrochemical impedance spectroscopy. II: Modelling

A common way to model lithium-ion batteries is to apply equivalent circuit (EC) models. In this work two different EC models are build up and parameterized for a commercial 6.5 Ah high-power lithium-ion cell. Measured impedance spectroscopy data depending on temperature and state of charge (SOC) are used for parameter estimation.The first EC model consists of an ohmic resistor (R), an inductor (L) and three RC-elements (a parallel connection of a capacitor (C) and a resistor). The second EC model consists of one R, one L, two Zarc elements and a Warburg element. The estimated parameters were used to develop two empirical electrical cell models which are able to predict the voltage of the cells depending on current, temperature and SOC. Hereby the internal cell resistance Ri is based on the EC models and a Butler-Volmer adjustment. Both approaches were validated by current profiles, which cover typical automotive applications to prove the model performance at low temperatures and high dynamic operation. An accurate voltage prediction could be realized with both EC models. The second, more complex, model is able to predict cell voltage more precisely, but at the expense of up to four times higher computational effort.     

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.     

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。     

Equalization of series connected lithium-ion batteries based on back propagation neural network and fuzzy logic control

In this article, a nondissipative equalization scheme is proposed to reduce the inconsistency of series connected lithium-ion batteries. An improved Buck-Boost equalization circuit is designed, in which the series connected batteries can form a circular energy loop, equalization speed is improved, and modularization is facilitated. This article use voltage and state of charge (SOC) together as equalization variables according to the characteristics of open-circuit voltage (OCV)-SOC curve of lithium-ion battery. The second-order RC equivalent circuit model and back propagation neural network are used to estimate the SOC of lithium-ion battery. Fuzzy logic control (FLC) is used to adjust the equalization current dynamically to reduce equalization time and improve efficiency. Simulation results show that the traditional Buck-Boost equalization circuit and the improved Buck-Boost equalization circuit are compared, and the equalization time of the latter is reduced by 34%. Compared with mean-difference algorithm, the equalization time of FLC is decreased by 49% and the energy efficiency is improved by 4.88% under static, charging and discharging conditions. In addition, the proposed equalization scheme reduces the maximum SOC deviation to 0.39%, effectively reducing the inconsistency of batteries.     

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。     

Thermal behaviors of Ni-MH batteries using a novel impedance spectroscopy

In this paper, a novel impedance spectroscopy was used to describe the thermal behaviors of Ni-MH batteries. The impedance functions were derived similarly to electric impedance functions. The square of current was treated as a current equivalent and heat-flow as a voltage equivalent. The impedance spectra of batteries during charge showed that the combination of hydrogen and oxygen increased rapidly when charge rate was higher than 0.5 C. Thermal runaway might happen when battery was charged at temperature above 348 K even at a low charge rate. The cycling test showed that the charge efficiency of battery was the highest after cycling at high-rate for 10–100 cycles and decreased after more cycles. Different batteries showed different thermal behaviors which may be caused by the different structures of batteries.     

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.     

Thermal explosion hazards of lithium-ion batteries in hermetic space

使用扩展容积加速度量热仪（extend volume accelerating rate calorimeter,EV-ARC）及耐压罐,开展了密闭空间中不同荷电状态（SOC）下18650型锂离子电池的热爆炸实验。实验发现,SOC=0%时电池不会发生热爆炸,而在其它工况下均发生了热爆炸;电池发生热爆炸时,电池表面最高温度、耐压罐内部最大压力都随着SOC的增加而增大。利用实验中电池发生热爆炸时的初始温度和最高温度,通过计算得到了不同SOC下电池发生热爆炸时的爆炸当量,当SOC=100%时,爆炸当量值最大,为5.45 gTNT,约是SOC=25%时的2.5倍,并在耐压罐中产生40.69 bar的峰值压力。锂离子电池在密闭中的热爆炸危险性随着电池SOC的增加而增大。     

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.     

Estimation of power battery SOC based on firefly BP neural network

针对BP神经网络算法对电动汽车电池荷电状态（state of charge,SOC）估算的缺陷,提出一种基于萤火虫（firefly algorithm,FA）神经网络的SOC估算方法。以磷酸铁锂电池为测试对象,在ARBIN公司生产的EVTS电动车动力电池测试系统装置上进行测试,收集锂电池的各项性能参数。采用端电压和放电电流作为输入参数,SOC作为输出参数,建立FA-BP神经网络模型,用于估算锂离子电池充放电过程中的任一状态下的SOC。仿真实验结果表明,与现有的BP神经网络估算方法相比,基于FA-BP神经网络的锂电池SOC估算方法准确度高,具备很好的实用性。     

Modeling of kinetic behavior of the lead dioxide electrode in a lead–acid battery by means of electrochemical impedance spectroscopy

In this paper a mathematical model for the electrochemical impedance of a positive electrode in the lead–acid battery was developed. The mechanisms of the electrode processes involved in the batteries were obtained from the literature. Having selected the rate-controlling step as well as the fast reversible (equilibrated) and irreversible steps, we embarked on the formulation of I–V behavior using Butler–Volmer and Fick's law for charge and mass transfer process, respectively. The equivalent circuit consists of resistors, capacitors and mass transfer elements. Each electrical element expresses physico-chemical parameters such as diffusion coefficient, concentration, rate constant, etc. So, impedance plots can be used to determine the effects of each parameter on the performance of the cells. The simulation model also shows that the state-of-charge (SOC) plays an important role in the Nyquist plot of the positive electrode. Model results are compared with experimental results for cell potential and different SOC.     

Experimental validation for Li-ion battery modeling using Extended Kalman Filters

The battery management systems (BMS) is an essential emerging component of both electric and hybrid electric vehicles (HEV) alongside with modern power systems. With the BMS integration, safe and reliable battery operation can be guaranteed through the accurate determination of the battery state of charge (SOC), its state of health (SOH) and the instantaneous available power. Therefore, undesired power fade and capacity loss problems can be avoided. Because of the electrochemical actions inside the battery, such emerging storage energy technology acts differently with operating and environment condition variations. Consequently, the SOC estimation mechanism should cope with the probable changes and uncertainties in the battery characteristics to ensure a permanent precise SOC determination over the battery lifetime.This paper aims to study and design the BMS for the Li-ion batteries. For this purpose, the system mathematical equations are presented. Then, the battery electrical model is developed. By imposing known charge/discharge current signals, all the parameters of such electrical model are identified using voltage drop measurements. Then, the extended kalman filter (EKF) methodology is employed to this nonlinear system to determine the most convenient battery SOC. This methodology is experimentally implemented using C language through micro-controller. The proposed BMS technique based on EKF is experimentally validated to determine the battery SOC values correlated to those reached by the Coulomb counting method with acceptable small errors.     

Inflection point Ah-total integration method for real-time integration to correct lithium battery SOC

对18650及26650磷酸铁锂电池的充放电电流、电压等数据分析表明：在电池循环老化过程中，虽然容量电压曲线两端曲率最大（拐点）处的SOC值有所变化，但是其电压保持不变。因此在估算SOC过程中，当放电电压达到拐点电压时，将此时的SOC修正为对应的拐点SOC，可以一定程度上优化安时积分法由于初始SOC而估算不准的问题。在此基础上提出一种新型的拐点修正安时积分算法，综合考虑温度、充放倍率、循环老化等因素对SOC估算精度的影响，引入充放电曲线拐点概念，建立SOC实时估算数学模型，减小消除安时积分法存在的累计误差问题。对比传统安时积分法估算精度，结果表明：SOC拐点修正安时积分实时估算法的误差在3%，说明该方法在实际工况中具有可行性，并且估算精度较高，可为SOC实时估算与检测提供重要参考。     

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.     

基于PNGV模型储能锂电池参数辨识及SOC估算研究

锂电池因具有比能量高、循环寿命长、对环境无污染等优点,在储能系统中已逐渐得到应用.准确估算锂电池的荷电状态(SOC)可防止电池过充、过放,保障电池安全、充分地使用.为了精确估算储能锂电池SOC,基于PNGV(partnership for a new generation of vehicles)电池等效模型,利用递推最小二乘法(RLS)对模型参数进行在线辨识和实时修正,增强了系统的适应性.结合安时法、开路电压法和PNGV模型,提出了一种实时在线修正SOC算法.根据实验数据,建立了仿真模型,以验算模型和SOC估算算法的精度.仿真结果表明,PNGV模型能真实地模拟电池特性,且能有效地提高SOC估算精度,适合长时间在线估算储能锂电池的SOC.     

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.