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.     

Online state of health prediction method for lithium-ion batteries,based on gated recurrent unit neural networks

Online state of health (SOH) prediction of lithium-ion batteries remains a very important problem in assessing the safety and reliability of battery-powered systems. Deep learning techniques based on recurrent neural networks with memory, such as the long short-term memory (LSTM) and gated recurrent unit (GRU), have very promising advantages, when compared to other SOH estimation algorithms. This work addresses the battery SOH prediction based on GRU. A complete BMS is presented along with the internal structure and configuration parameters. The neural network was highly optimized by adaptive moment estimation (Adam) algorithm. Experimental data show very good estimation results for different temperature values, not only at room value. Comparisons performed against other relevant estimation methods highlight the performance of the recursive neural network algorithms such as GRU and LSTM, with the exception of the battery regeneration points. Compared to LSTM, the GRU algorithm gives slightly higher estimation errors, but within similar prediction error range, while needing significantly fewer parameters (about 25% fewer), thus making it a very suitable candidate for embedded implementations.     

Review on state of health estimation of retired lithium-ion batteries

由于电池组中电池单体之间存在性能差异,退役锂离子电池在投入梯次利用前需要借助健康状态（SOH）评估技术进行电池单体的分类与配组。健康状态评估系统的构建涉及电池建模、电池测试、数据处理、算法开发等各种技术问题。目前通过基于模型的参数识别与直接提取健康因子是构建SOH评估体系的两种主要思路。在电池模型的简化、测试工况的设计、健康因子的选择和算法的应用与优化等方面已经有了很多研究。如何在缩短电池测试时间的同时提高评估系统的泛化能力是目前该研究领域的主要问题,这些问题的解决对于SOH评估系统真正在梯次利用锂离子电池的产业化中发挥作用至关重要。在未来的研究中通过优化测试工况和数据融合等技术,有望开发出性能更好的SOH评估系统。     

Lithium-ion battery SOC/SOH adaptive estimation via simplified single particle model

Compared with battery Equivalent Circuit Models (ECM), Single Particle Model (SPM) has more appropriate physics representation and higher accuracy theoretically. However, SPM-based parameter estimation performance is restricted by the SPM model complexities. In this paper, a simplified SPM and its corresponding adaptive State of Charge (SOC)/State of Health (SOH) estimation scheme are studied. First, the SPM is simplified from Partial Differential Equation (PDE) to Ordinary Differential Equation (ODE) for a trade-off between model complexity and consistency. Second, an adaptive model observer is proposed to estimate battery parameters, which include a SOC state implying normalized lithium-ion concentration, and a SOH parameter implying the maximum lithium-ion surface concentration, both in the solid surface phase. Because the ODE-based adaptive parameter estimation is capable of avoiding complex identification procedures, this new approach can be implemented in practical applications with high accuracy. Through massive simulation scenarios, the proposed SPM model is validated based on comparison between ODE SPM and PDE SPM, as well as Benchmark Validation. Finally, both simulation and experiment demonstrate the effectiveness of the simplified SPM and the superiority of the proposed SOC/SOH estimation scheme.     

基于磷酸铁锂电池变电站直流系统BMS的研究与应用

磷酸铁锂电池管理单元（BMS）是文中研究的重点,如何把握电池内部状态的变化规律以及外部因素对电池容量的影响、建立合理有效的电池模型和SOC算法、实现SOC在线估计并减少估算误差,是电池安全管理最基本、最重要的方面。电池管理单元（BMS）与变电站直流系统监控器通过CAN通信,能有效的保证磷酸铁锂电池组及整个直流系统安全可靠的工作。     

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.     

Online state-of-health prediction of lithium-ion batteries with limited labeled data

State-of-health (SOH) plays a vital role in battery health management and power system stability. This process can be achieved by capacity estimation. However, in practice, the capacity of a battery is difficult to obtain online given that it cannot be determined with general sensors. This means that the capacity is only known for the limited cycles of the batteries. To address this issue, we propose a novel semi-supervised learning framework to estimate the capacity of unlabeled data to achieve better SOH prediction. First, four indirect features are extracted from the charging profiles. Then an improved locally linear reconstruction method is used to determine the capacity distributions of the unlabeled data. Combined with the oversampling method applied to generate a series of data by the estimated distributions, a support vector regression model is utilized to predict the RUL of the batteries given the threshold values of the batteries. A case study with two types of cellular phone lithium-ion batteries is presented to illustrate the effectiveness of the proposed method for the prediction of the remaining useful life of different batteries and different starting points. The experimental results prove that the performance of the proposed method is better than the K-nearest neighbor method and locally linear reconstruction method in terms of accuracy and robustness.     

Remaining useful life prediction of lithium-ion battery based on extended Kalman particle filter

Scientific estimation and prediction of the state of health (SOH) of lithium-ion battery, especially the remaining useful life (RUL), has important significance to guarantee the battery safety and reliability in the full life cycle to avoid catastrophic accidents as much as possible. In order to accurately predict the RUL of the lithium-ion battery, this paper firstly analyzes the problems of the standard particle filter (PF). Then, a novel extended Kalman particle filter (EKPF) is proposed, in which the extended Kalman filter (EKF) is used as the sampling density function to optimize PF algorithm. The life cycle tests are designed and carried out to get accurate and reliable data for the RUL prediction. And, the aging properties of lithium-ion battery are analyzed in detail. The RUL prediction is done based on the established capacity degradation model and the proposed EKPF method. Results show that the RUL prediction error of the proposed method is less than 5%, which has higher precision compared with the standard PF method and can be used both offline and online.     

Comparison of data-driven lithium battery state of health estimation methods

回顾了人工神经网络、支持向量回归、高斯过程回归三种主流数据驱动方法在动力电池健康状态（stateof health,SOH）估算方面的研究进展。人工神经网络适合模拟动力电池,能达到很高的精度;支持向量回归计算量小,理论基础完善,在动力电池SOH估算研究中应用广泛;高斯过程回归精度高并能给出预测结果的置信区间,近年相关文献数量呈现增长趋势。针对现行SOH定义未能反映锂电池额定电压衰退的弊端,提出了利用电池满充能量定义SOH。进而分别建立了BP神经网络、支持向量回归、高斯过程回归模型,利用新能源汽车大数据,对电池充电能量进行了预测,定量对比结果验证了三种方法在计算量和精确度方面的特点。最后展望了数据驱动方法与新能源汽车大数据在动力电池SOH估算研究方面的应用前景。     

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.     

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.     

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.     

A new dynamic SOH estimation of lead‐acid battery for substation application

State of Health (SOH) is one of the most important parameters of lead‐acid batteries. Most of the existing SOH estimation methods only take the influence of charge cycles into consideration, and the estimation accuracy is limited. Batteries in the substations have two typical states: one is the check‐discharge state, in which the batteries are discharged for 8 h at 0.1 C (Capacity) to determine whether the battery pack has certain reliability. The other is the floating charge state, in which the batteries are connected to the charger to maintain full power. This paper proposes a novel SOH estimation method based on the two states. In the check‐discharge state, the relationship between the voltage and the age of battery is analysed. The health index, which is introduced in this model, is affected by the age of battery. In the floating state, the relationship between the internal resistance and the age of battery is discussed. Another SOH model is established based on the change of the internal resistance. By combining the two models, the estimation method can achieve real‐time estimation and high accuracy for substation application. An accelerated life test is applied to verify the theoretical analysis. The experimental results demonstrate that the SOH estimation error is less than 3% which is very satisfactory for practical applications. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Estimation of battery available capacity under variable discharge currents

In this paper, a new mathematical model in semi-empirical form for lead-acid batteries is presented, which describes the relationship between the battery terminal voltage and the variable discharge current. Based on the proposed model, a new estimation method of the battery available capacity (BAC) in the presence of variable discharge currents is developed. The method involves the real-time identification of the model parameters which are then used to estimate the BAC according to the predefined cutoff voltage and the trend of battery terminal voltage during discharging. Thus, both temperature and aging influences on the BAC are considered inherently. Comparisons between the calculated results and the measured data confirm that the proposed method can provide an accurate real-time estimation of the BAC under variable discharge currents.     

Aging model development based on multidisciplinary parameters for lithium-ion batteries

In this paper, a method composed of state of health (SOH) testing experiments and artificial intelligence simulation is proposed to carry out the study on the change of battery characteristic during its operation and generate mathematical models for the prediction of aging behaviour of battery. An experiment comprising of multidisciplinary parameters-based SOH detection is conducted to study the battery aging characteristics from several aspects (ie, electrochemistry, electric, thermal behaviour and mechanics). In total, 200 sets of data (corresponding 200 charging/discharging cycles) are collected from the experiment. The data obtained from the first 150 cycles are employed in generation of the models. The result of sensitivity analysis based on the obtained genetic programming models shows that it is better to apply voltage value at the end of charging step, charging time and cycle number to predict the operational performance of the battery. The average predicted accuracy of model (without stress) is 94.52%, whereas the average predicted accuracy of model (with stress effect) is 99.42%. The proposed models could be useful for defining the optimised charging strategy, fault diagnosis and spent batteries disposal strategies.     

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.     

Online estimation of model parameters and state-of-charge of LiFePO4 batteries in electric vehicles

The accurate estimation of internal parameters and state-of-charge (SoC) of battery, which greatly depends on proper models and corresponding high-efficiency, high-accuracy algorithms, is one of the critical issues for the battery management system. A model-based online estimation method of a LiFePO₄ battery is presented for application in electric vehicles (EVs) by using an adaptive extended Kalman filter (AEKF) algorithm. The Thevenin equivalent circuit model is selected to model the LiFePO₄ battery and its mathematics equations are deduced to some extent. Additionally, an implementation of the AEKF algorithm is elaborated and employed for the online parameters’ estimation of the LiFePO₄ battery model. To illustrate advantages of the online parameters’ estimation, a comparison analysis is performed on the terminal voltages between the online estimation and the offline calculation under the Hybrid pulse power characteristic (HPPC) test and the Urban Dynamometer Driving Schedule (UDDS) test. Furthermore, an efficient online SoC estimation approach based on the online estimation result of open-circuit voltage (OCV) is proposed. The experimental results show that the online SoC estimation based on OCV-SoC can efficiently limit the error below 0.041.     

5kW锂电池模组BMS的研究与开发

设计了以MSP430为控制核心的用于5 k W锂电池管理系统(BMS).建立了关于电池荷电状态的模型,在实际估计中,采用开路电压和按时积分相结合的方法且有较高的精度;采取电池均衡充电的方案,补偿了电池容量的差异性,进而使得电池组的使用寿命延长.电池荷电状态估算的改进方案解决了按时计量法无法确定初始荷电状态、难以精准测得库仑效率等问题,确保了电池管理系统处于稳定工作状态.该系统具有抗干扰能力极强、硬件电路可靠、且十分经济的特点.经过实验验证,利用该系统进行SOC剩余容量估计的结果较为精确.     

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.