Two‐layer online state‐of‐charge estimation of lithium‐ion battery with current sensor bias correction

Because of the harsh working condition in electrified vehicles, the measured current and voltage signals typically contain non‐ignorable noises and bias, which potentially decline the accuracy of state‐of‐charge estimation. In this regard, the noise and bias corruption should be well addressed to maintain sufficient accuracy and robustness. This paper improves the existing methods in the literature from two aspects: (a) A novel offset‐free equivalent circuit model is developed to remove the current bias; and (b) based on the offset‐free equivalent circuit model, a two‐layer estimator is proposed to estimate the state of charge using real‐time identified model parameters. The robustness of the two‐layer estimator against model uncertainties and the aging effect is further evaluated. Simulation and experimental results show that the proposed two‐layer estimator can effectively attenuate the current bias and estimate the state of charge accurately with the error confined to ±4% under different levels of current bias and model uncertainties.     

A model‐based and data‐driven joint method for state‐of‐health estimation of lithium‐ion battery in electric vehicles

Lithium‐ion battery state‐of‐health estimation is one of the vital issues for electric vehicle safety. In this work, a joint model‐based and data‐driven estimator is developed to achieve accurate and reliable state‐of‐health estimation. In the estimator, an increase in ohmic resistance extracted from the Thevenin model is defined as the health indicator to quantify the capacity degradation. Then, a linear state‐space representation is constructed based on the data‐driven linear regression. Furthermore, the Kalman filter is introduced to trace capacity degradation based on the novel state space representation. A series of battery aging datasets with different dynamic loading profiles and temperatures are obtained to demonstrate the accuracy and robustness of the proposed method. Results show that the maximum error of the Kalman filter is 2.12% at different temperatures, which proves the effectiveness of the proposed method.     

Online parameters identification and state of charge estimation for lithium‐ion batteries using improved adaptive dual unscented Kalman filter

State of charge (SOC) is a vital parameter which helps make full use of battery capacity and improve battery safety control. In this paper, an improved adaptive dual unscented Kalman filter (ADUKF) algorithm is adopted to realize co‐estimation of the battery model parameters and SOC. Notably, the covariance matching method that can adapt the system noise covariance and the measurement noise covariance is used to improve the estimation accuracy. Besides, singular value decomposition (SVD) is utilized to deal with the non‐positive error covariance matrix in both unscented Kalman filters, further enhancing the stability of estimation algorithm. Verification results under Dynamic Stress test and Federal Urban Driving Schedule test indicate that improved ADUKF can achieve more accurate SOC estimates with error band controlled within 2.8%, while that of traditional dual unscented Kalman filter (DUKF) can only be controlled within 5%. Moreover, robustness analysis is also conducted and the validation results present that the proposed algorithm can still provide precise SOC prediction results under some disturbances, such as erroneous initial SOC, inaccurate battery capacity, and various ambient temperatures.     

State‐of‐charge estimation of power lithium‐ion batteries based on an embedded micro control unit using a square root cubature Kalman filter at various ambient temperatures

The development of a novel method to estimate the state of charge (SOC) with low read‐only memory (ROM) occupancy, high stability, and high anti‐interference capability is very important for the battery management system (BMS) in actual electric vehicles. This paper proposes the square root cubature Kalman filter (SRCKF) with a temperature correction rule, based on the BMS of a common on‐board embedded micro control unit (MCU), to achieve smooth estimation of SOC. The temperature correction rule is able to reduce the testing effort and ROM space used for data table storage (189.3 kilobytes is much smaller than the storage of the MPC5604B, with 1000 kilobytes), while the SRCKF is adopted to achieve highly robust real‐time SOC estimation with high resistance to interference and moderate computing cost (68.3% of the load rate of the MPC5604B). The results of multiple experiments show that the proposed method with less computational complexity converges rapidly (in approximately 2.5 s) and estimates the SOC of the battery accurately under dynamic temperature condition. Moreover, the SRCKF algorithm is not sensitive to the high measuring interference and highly nonlinear working conditions (even with 1% current and voltage measurement disturbances, the root mean square error of the proposed method can be as high as 0.679%).     

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.     

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.     

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.     

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.     

Least‐squares based coulomb counting method and its application for state‐of‐charge (SOC) estimation in electric vehicles

Coulomb counting method is a convenient and straightforward approach for estimating the state‐of‐charge (SOC) of lithium‐ion batteries. Without interrupting the power supply, the remaining capacities of them in an electric vehicle (EV) can be calculated by integrating the current leaving and entering the batteries. The main drawbacks of this method are the cumulative errors and the time‐varying coulombic efficiency, which always lead to inaccurate estimations. To deal with this problem, a least‐squares based coulomb counting method is proposed. With the proposed method, the coulombic losses can be compensated by charging/discharging coulombic efficiency η and the measurement drift can be amended with a morbid efficiency matrix. The experimental results demonstrated that the proposed method is effective and convenient. 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.     

State‐of‐charge estimators considering temperature effect,hysteresis potential,and thermal evolution for LiFePO4 batteries

To achieve accurate state‐of‐charge (SoC) estimation for LiFePO₄ batteries, the effects of temperature, hysteresis, and thermal evolution are elaborately modeled. Open‐circuit voltage is regarded as the sum of electromotive force and hysteresis potential (V_h), where electromotive force is constructed as the function of SoC and temperature and V_h is reproduced with a geometrical model. By simulating battery heat generation and dissipation, a thermal evolution model is established and exploited for open‐circuit voltage and parameter identification. Then, on the basis of a second‐order equivalent circuit model, 2 SoC estimation schemes are proposed: One scheme uses the recursive least square with forgetting factor algorithm and off‐line equivalent circuit model parameters derived by the differential evolution algorithm; the other scheme resorts to the adaptive extended Kalman filter (EKF) and online tuned parameters. Experiments validate the effectiveness of the hysteresis model and the thermal evolution model. In contrast to a joint EKF estimator, experimental results under different temperatures and initial states suggest that both the proposed estimators are superior to the joint EKF estimator. Benefiting from the online updated parameters, the adaptive EKF estimator behaves best for giving consistent SoC‐tracking performance under different conditions.     

A method for remaining discharge time prediction of lithium‐ion batteries under dynamic uncertainty

Remaining discharge time of the battery system in electric vehicles relates strongly to the decision‐making of driving. Subjected to the various uncertainties, such as modeling uncertainty, state estimation uncertainty, and future load uncertainty, the accuracy and reliability of the remaining discharge time prediction reduce, which will lead to range anxiety. A stochastic framework based on the state‐of‐charge estimation and prediction strategy is proposed to predict remaining discharge time against the uncertainty. Firstly, the equivalent circuit model is established to model the dynamic behavior of the battery. Through the analysis of different fitting functions of open circuit voltage and state‐of‐charge, the Akaike information criterion is introduced to select the best function. Secondly, the coestimator is employed to bound the influence of the model parameter uncertainty and noise uncertainty. Finally, the uncertainties are quantified by a probabilistic method, and a Monte Carlo–based stochastic prediction strategy is proposed to predict the probability distribution of remaining discharge time under dynamic uncertainty. Experimental results demonstrate that the proposed prediction framework is of great effectiveness as it can provide an accurate remaining discharge time interval under dynamic uncertainty, which helps to promote the energy‐saving driving and overcome the range anxiety.     

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.     

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.     

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.     

An alternating current heating method for lithium‐ion batteries from subzero temperatures

An alternating current (AC) heating method for lithium‐ion batteries is proposed in the paper. Effects of current frequency, amplitudes and waveforms on the temperature evolution and battery performance degradation are respectively investigated. First, a thermal model is established to depict the heat generation rate and temperature status, whose parameters are calibrated from the AC impedance measurements under different current amplitudes and considering battery safe operating voltage limits. Further experiments with different current amplitudes, frequencies and waveforms on the 18650 batteries are conducted to validate the effectiveness of the AC heating. The experimental data recorded by appropriate measurement instrument are of great consistence with simulation results from the thermal model. At high frequency, the temperature rises prominently as the current increases, and high frequency serves as a good innovation to reduce the battery degradation. However, efficient temperature rise can be obtained from high impedance at low frequencies. Typically, 600 s is needed to heat up the battery from ?24 °C to 7.79 °C with sinusoidal waveform and approximately from ?24 °C to 25.6 °C with rectangular pulse waveform at 10A and 30 Hz. The model and experiments presented have shown potential value in battery thermal management studies for electric vehicle (EV)/hybrid electric vehicle (HEV) applications at subzero temperatures. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Study of relationship between temperature and thermal energy,operating conditions as well as environmental factors in large‐scale lithium‐ion batteries

We have developed a thermal model for a large‐scale lithium‐ion cell and have simulated its thermal behaviors during charge, discharge, and charge–discharge cycles with different current rates by using the software of COMSOL Multiphysics 3.5a. In this work, thermal energy and its distribution were firstly calculated based on experimental data under different operating conditions. A new parameter, called thermal energy conversion efficiency, was proposed to describe relative value of thermal energy in the cell. The thermal energy conversion efficiency and the temperature were plotted in a figure to show their relativity. The temperature variation was also studied systemically when the cell underwent discharge–charge cycles. A low rate charge is validated to be a favorable factor in protecting the cell from overheating during charge–discharge cycles. A connection resistance is proved to be a main factor that accelerates the rise of temperature in the spot near a terminal column, which should be eliminated as much as possible to protect the cell from local overheating. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

A wavelet transform‐adaptive unscented Kalman filter approach for state of charge estimation of LiFePo4 battery

LiFePo₄ battery is widely used in electric vehicles; however, its flatness and hysteresis of the open‐circuit voltage curve pose a big challenge to precise state of charge (SOC) estimation. The issue is discussed and addressed in this paper. First, a cell model with hysteresis is built to describe real‐time dynamic characteristics of the LiFePo₄ battery. Second, the model parameters and SOC are estimated independently to avoid the possibility of cross interference between them. For model identification, an adaptive unscented Kalman filter (AUKF) algorithm is used to identify the cell parameters as they change slowly. While SOC could change rapidly, wavelet transform AUKF algorithm is put forward to estimate SOC. In the novel algorithm, the measurement noise can be estimated and updated online. Finally, the performance of the proposed method is verified under dynamic current condition. The experimental results show that estimated value based on the proposed method is more accurate than unscented Kalman filter‐based method and AUKF‐based algorithm. Meanwhile, the proposed estimator also has the merits of fast convergence and good robustness against the initialization uncertainty.