Abstract
Purpose
The operation state of lithium-ion battery for vehicle is unknown and the remaining life is uncertain. In order to improve the performance of battery state prediction, in this paper, a joint estimation method of state of charge (SOC) and state of health (SOH) for lithium-ion batteries based on multi-scale theory is designed.
Design/methodology/approach
In this paper, a joint estimation method of SOC and SOH for lithium-ion batteries based on multi-scale theory is designed. The venin equivalent circuit model and fast static calibration method are used to fit the relationship between open-circuit voltage and SOC, and the resistance and capacitance parameters in the model are identified based on exponential fitting method. A battery capacity model for SOH estimation is established. A multi-time scale EKF filtering algorithm is used to estimate the SOC and SOH of lithium-ion batteries.
Findings
The SOC and SOH changes in dynamic operation of lithium-ion batteries are accurately predicted so that batteries can be recycled more effectively in the whole vehicle process.
Originality/value
A joint estimation method of SOC and SOH for lithium-ion batteries based on multi-scale theory is accurately predicted and can be recycled more effectively in the whole vehicle process.
Keywords
Citation
Li, P., Wang, H., Xing, Z., Ye, K. and Li, Q. (2020), "Joint estimation of SOC and SOH for lithium-ion batteries based on EKF multiple time scales", Journal of Intelligent Manufacturing and Special Equipment, Vol. 1 No. 1, pp. 107-120. https://doi.org/10.1108/JIMSE-09-2020-0008
Publisher
:Emerald Publishing Limited
Copyright © 2020, Peiqing Li, Huile Wang, Zixiao Xing, Kanglong Ye and Qipeng Li
License
Published in Journal of Intelligent Manufacturing and Special Equipment. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode
1. Introduction
The on-board battery is the main energy supply unit to drive the electric vehicle. The battery can provide the energy required for vehicle driving power and can also provide energy support for the electronic system of the whole vehicle. At the same time, the performance indexes related to the energy, power and multiplying power characteristics of the battery also significantly affect the performance of the vehicle. Therefore, the battery management system (BMS) and its key technology of real-time control module become the research focus of vehicle battery performance and battery monitoring system optimization (Yang et al., 2019; Al-Zareer et al., 2018; Zheng, 2017; Zhou, 2016; Ye et al., 2020). In order to ensure the endurance of electric vehicle and protect the running state of battery pack at the same time, the collaborative estimation of state of charge (SOC), state of health (SOH), remaining useful life (RUL) and other issues of on-board battery is gradually becoming the focus of domestic and foreign scholars (Ma et al., 2019; He et al., 2015; Pattipati et al., 2011).
The accurate estimation of SOC of lithium battery is studied in Zhang et al. (2018), Awadallah and Venkatesh (2016), Alfi et al. (2014), Charkhgard and Farrokhi (2010), Chen et al. (2013), He et al. (2011). Zhang et al. (2018), Awadallah and Venkatesh (2016), Alfi et al. (2014) used the neural network, learning algorithm and other different methods to accurately estimate the SOC of lithium battery. And the advantages and disadvantages of different methods are discussed. Extended Kalman filtering was applied to estimate the SOC of lithium-ion battery in Charkhgard and Farrokhi (2010), Chen et al. (2013), He et al. (2011). Chaoui et al. (2015), Gholizadeh and Salmasi (2014) jointly considers the SOC and SOH of lithium batteries, and Chaoui et al. (2015) proposes an adaptive strategy to estimating online parameters of the battery model using a Lyapunov-based adaptation law. Gholizadeh and Salmasi (2014) also consider inclusive models, using analytical methods to estimate additional non-linear or uncertainty terms in the model. This approach provides a very accurate model of the battery used in a battery management system. In addition, an online parameter estimation method is proposed to estimate the operating condition of the battery. Kim and Cho (2011), Kim et al. (2012) studies on the synergistic control of both SOC and SOH have used Kalman filtering combined with neural networks for the identification of cell models.
The coordinated control of SOC and SOH of battery is one of the important indicators to realize the balance of BMS. Although many scholars have done research in battery SOC control, but the synergistic control of SOC and SOH is still ineffective. Poor control can even reduce the driving performance of the vehicle, leading to a reduction in the life of the complete vehicle battery and the unknown safety of its use (Tong et al., 2015; Yan et al., 2019; Cannarella and Arnold, 2014). Predicting battery aging decay is one of the main difficulties in battery management, and studies have shown that the decay of SOH is closely related to factors such as temperature, cycle times, charge/discharge depth and current. Therefore, accurate real-time online monitoring by SOH can provide effective support for the balanced regulation of vehicle batteries (Chen et al., 2020; Zhang et al., 2020; Murariu and Morari, 2019). From the actual vehicle operating environment, it can be concluded that SOC is one of the influencing parameters for studying and evaluating SOH attenuation.
2. Method based on analysis model
2.1 Establishment of aging model of lithium-ion battery
Li-ion battery packs will suffer from self-discharge and leakage due to prolonged outage and the actual SOC value will also be inaccurate. The relationship between capacity and charge discharge times can be obtained by aging model of lithium-ion battery (Wei et al., 2019; Ishizaki et al., 2015). In this paper, the typical exponential model is selected to build the corresponding aging model, and the capacity decay data in the process of battery charging and discharging are used to fit continuously. The corresponding exponential aging model is described as shown in Eqn. (1).
The equivalent circuit model consists of three parts: the equivalent analysis of the model, the correlation between OCV and SOC and the identification of resistance and capacitance parameters (Lin et al., 2017). Based on the analysis of short-term capacity aging characteristics, a capacity model and an aging model are established to fit the change trend of vehicle battery in the aging process. At the same time, comparing the exponential model with the polynomial model, it is not difficult to find that the exponential model is more suitable for building the corresponding aging model.
2.2 Equivalent model of lithium-ion battery
To establish a battery equivalence model, the main parameters of the model are needed to be obtained, i.e. internal variables, capacity, internal resistance and other characterization parameters of the battery. Predicting SOH by the developed model can get the value of SOH more directly. However, the disadvantage of pre-processing the measurement data makes it difficult to balance efficiency and real-time performance (Song et al., 2020; Stroe and Schaltz, 2020). At the same time, due to the accuracy of estimation, the estimation methods based on the equivalent model method and electrochemical method cannot be directly used in other batteries. In the case of stable working environment, the method based on experience and characteristics will have a good performance. Due to the special dependence of the empirical model and the characteristic model, it cannot perform well under complex conditions. With the convenience of data acquisition and storage, data-based methods have become common, which can also predict the SOH of the battery and eliminate the fault. The method also suffers from certain shortcomings due to the time-consuming nature of data collection and the variability of working conditions (Ye and Li; Liu et al., 2018; Roscher and Sauer, 2011). The different methods mentioned above have their own advantages and disadvantages. In this paper, based on the research of domestic and foreign scientific and technological workers, the applicability, high precision and real-time characteristics of the direct method will be combined to carry out online capacity prediction, so as to directly calculate the corresponding SOH value.
By using Kirchhoff's current and voltage theorem, the parameters of Thevenin equivalent circuit model (as shown in Figure 1) can be obtained from Eqns. (2) and (3).
Take
For (5) and (6) discretization, the sampling time interval
Eqns. (7) and (8) are the state space equations corresponding to the equivalent circuit model, on which the SOC estimator can be designed. In order to obtain the values of the variables in the model parameters, an improved fitting method is adopted and used in this paper to fit the relationship between SOC and OCV, while the use of the end-voltage exponential fit will further yield the values of capacitance and resistance in the equivalent model. The exact OCV-SOC relationship is shown in Figure 2.
By fitting the relationship between open circuit voltage and SOC, the following expression can be obtained.
In this paper, the method of exponential fitting is used to identify the capacitive resistance parameters in Eqns. (7) and (8). The root mean square error and standard deviation obtained using least squares are the smallest of the terms, accurate and closer to the BMS reaction time. Through the reasonable analysis of the output equation of the battery, the exponential function fitting method is used in this paper to fit the trend of voltage change in the region of current mutation. Finally, according to the relationship between the fitted variables and the resistance value, the capacitance value
Similarly, due to the need of parameter identification, this paper uses exponential function to fit Eqn. (11).
The fitting result is shown in Figure 3. The blue curve is the voltage curve of the fitting result, and the red curve is the actual measured value during operation. It can be seen from the figure that the change curve of battery voltage predicted by the model is highly consistent with the actual situation, indicating that the identification result can accurately reflect the state change during the operation of the battery.
The exponential fit yields the following values for the variables
Among them, it can be calculated that
2.3 Establishment of capacity model of lithium-ion battery
The change of the rated capacity of the battery shows the change of its SOH, that is, the prediction of SOH can be made by estimating the rated capacity of the battery. Therefore, it is necessary to establish the corresponding model for estimating the battery capacity, that is, the capacity model. Considering that the battery capacity changes in a short period of time are relatively small, the capacity changes can be expressed as follows.
Generally, current and terminal voltage can be measured directly from a battery system. Therefore, in the capacity prediction system, the terminal voltage is chosen as the output variable and the current as the input variable. The output equation of the corresponding equivalent circuit model is also the output equation of the battery capacity model, that is, the above Eqn. (16) is also the output equation of the capacity model.
3. Prediction method based on multi time scale theory
Due to the aging and performance deterioration caused by the use of batteries, the external performance shows the decline of capacity and power. In the energy management of electric vehicle battery, the health status of battery is evaluated by the number of cycles, battery voltage and internal resistance parameters under full saturation state. If any of these variables reach the threshold value, the vehicle battery can be judged to be in dangerous operation (Farjah and Ghanbari, 2020; Han et al., 2014).
In this paper, SOH is calculated by the common judgment method of current research capacity, that is, the ratio of the maximum amount of electricity released by the battery in the use of the vehicle to the factory capacity marked on the nameplate of the vehicle battery, as shown in Eqn. (17).
As expected SOC in vehicle environment, SOH is also a nonlinear time-varying system. Environmental temperature and humidity, service speed, over discharge and service cycle are all factors that affect the prediction of SOH.
3.1 Multi-time scale estimation
3.1.1 Multi-time scale EKF model transformation
Multi-time scale analysis is based on the establishment of multi-scale theory, which reflects the change of variables in different dimensions and multi-scale research on the research object, with multi-scale characteristics. Compared with the change of the rated capacity of vehicle battery, the SOC of vehicle battery changes more frequently in the use of vehicle battery. Especially in the condition of high current charging and discharging, the driving moment can change a lot. However, since the change of vehicle battery SOH is very slow, there is no obvious change in the initial stage of use, indicating that the time changes of SOC and SOH scale are different. The error inevitably increases if the SOC projections and the SOH status are studied at the same scale (Hu et al., 2020; Zou et al., 2016; Hua et al., 2015). In order to reduce the deviation and simplify the calculation of the estimator, a multi-time scale estimation method is designed to realize the joint estimation of SOC and SOH of vehicle battery. Establishing macro and micro scales of measurement to estimate the rated capacity of vehicle batteries at the macro scale and at the frequently changing micro time scale. The SOC of the vehicle battery is estimated on. polarization response voltage, as a macroscopic scale variable. Transformation of the established state space model allows to obtain a mathematical model description.
3.1.2 Multi time scale EKF algorithm
In the multi-time scale framework, SOC and SOH of vehicle battery are predicted based on EKF. SOC of vehicle battery is observed at micro scale, while SOH is predicted at macro scale. For the convenience of research,
The algorithm steps of multi time scale EKF are as follows.
For initial time as
Initializing the multiscale EKF.
For
Updating the time of
For
Updating the time of
Updating measurement of
Extracting battery status.
Calculating time series.
When
Converting timescale.
For
Updating measurement of
Extracting of the rated capacity of battery.
Matrices
4. Comparative analysis of experiments and results
4.1 Algorithm verification under vehicle test condition
In this paper, new European driving cycle (NEDC), New York city cycle (NYCC) and urban dynameter driving schedule (UDDS) are used to verify the joint estimation algorithm under different vehicle states. The operation of the three conditions is shown in Figure 5.
4.2 Analysis of experimental results
During the experiment, the initial SOC value of vehicle battery is 0.8, and the rated capacity of new battery nameplate is 27 Ah (SOH = 0.93). In order to test the robustness of the designed estimator when the initial value is biased, the SOC initial value of the designed estimator is set as 0.9, the initial capacity value is 26.3 Ah (SOH = 0.912). The scale variable of multi time scale algorithm L is 100. On the macro time scale, time and measurement are updated every
Based on advisor simulation platform, the simulation results of battery are shown in Figure 6.
(a) Represents the simulation results under NEDC condition. The first block diagram shows the end voltage and current variation curve of vehicle battery, the second block diagram represents the estimated battery SOC estimation value, and in the third block diagram, the blue curve represents the end voltage curve of vehicle battery unit, and the red curve represents the error change. The fourth block diagram shows the change of capacity and deviation curve of SOH. It can be seen from the second block diagram that the estimation error is less than 0.3%. In the initial stage of 200s, due to setting the initial value of deviation from the actual value, the estimation result error is obvious, and the deviation gradually decreases with the increase of operation time. In the fourth block diagram, in the rated capacity variation curve, there is a large deviation between the estimated capacity and the actual value at the initial moment, and the error gradually converges with time, and the estimation accuracy deviation is always kept in a small range.
(b) Represents the simulation results under NYCC condition. The first block diagram is voltage and current curve, the second block diagram is SOC and single voltage, and the second block diagram is battery operating temperature. The estimated curve in the figure always coincides with the actual measured result. The second block diagram shows that the accuracy of SOC and capacity estimation of vehicle battery has practical engineering application.
(c) Represents the simulation results under UDDS condition. The three block diagrams in the figure are the same as those of (b). The diagram shows that the loop test is stable.
5. Conclusion
In this paper, a joint estimation method of SOC and SOH based on multi time scale EKF algorithm is proposed. The multi time scale EKF algorithm is analyzed, in which the macro EKF is used to estimate the rated capacity and the micro EKF is used to estimate the SOC. A multi-scale algorithm estimator with high computational frequency and small computational size is designed, and the rationality of the algorithm is verified by simulation under working conditions. As can be seen from the experimental simulation curves, the multi-timescale EKF algorithm can be implemented very accurately to measure the lithium-ion battery status and remaining life of the vehicle.
Figures
References
Al-Zareer, M., Dincer, I. and Rosen, M.A. (2018), “A review of novel thermal management systems for batteries”, International Journal of Energy Research, Vol. 42 No. 10, pp. 3182-3205.
Alfi, A., Charkhgard, M. and Zarif, M.H. (2014), “Hybrid state of charge estimation for lithium-ion batteries: design and implementation”, IET Power Electronics, Vol. 7 No. 11, pp. 2758-2764.
Awadallah, M.A. and Venkatesh, B. (2016), “Accuracy improvement of SOC estimation in lithium-ion batteries”, Journal of Energy Storage, Vol. 6, pp. 95-104.
Cannarella, J. and Arnold, C.B. (2014), “State of health and charge measurements in lithium-ion batteries using mechanical stress”, Journal of Power Sources, Vol. 269, pp. 7-14.
Chaoui, H., Golbon, N., Hmouz, I., Souissi, R. and Tahar, S. (2015), “Lyapunov-based adaptive state of charge and state of health estimation for lithium-ion batteries”, IEEE Transactions on Industrial Electronics, Vol. 62 No. 3, pp. 1610-1618.
Charkhgard, M. and Farrokhi, M. (2010), “State-of-charge estimation for lithium-ion batteries using neural networks and EKF”, IEEE Transactions on Industrial Electronics, Vol. 57 No. 12, pp. 4178-418.
Chen, Z., Fu, Y.H. and Mi, C.C. (2013), “State of charge estimation of lithium-ion batteries in electric drive vehicles using extended Kalman filtering”, IEEE Transactions on Vehicular Technology, Vol. 62 No. 3, pp. 1020-1030.
Chen, L., Tong, Y.Q. and Dong, Z.M. (2020), “Li-ion battery performance degradation modeling for the optimal design and energy management of electrified propulsion systems”, Energies, Vol. 13 No. 7, p. 136070.
Farjah, A. and Ghanbari, T. (2020), “Early ageing detection of battery cells in battery management system”, Electronics Letters, Vol. 56 No. 12, pp. 616-618.
Gholizadeh, M. and Salmasi, F.R. (2014), “Estimation of state of charge, unknown nonlinearities, and state of health of a lithium-ion battery based on a comprehensive unobservable model”, IEEE Transactions on Industrial Electronics, Vol. 61 No. 3, pp. 1335-1344.
Han, X.B., Ouyang, M.G., Lu, L.G., Li, J.Q., Zheng, Y.J. and Li, Z. (2014), “A comparative study of commercial lithium ion battery cycle life in electrical vehicle: aging mechanism identification”, Journal of Power Sources, Vol. 251, pp. 28-54.
He, H.W., Xiong, R., Zhang, X.W., Sun, F.C. and Fan, J.X. (2011), “State-of-charge estimation of the lithium-ion battery using an adaptive extended Kalman filter based on an improved Thevenin model”, IEEE Transactions on Vehicular Technology, Vol. 60 No. 4, pp. 1461-1469.
He, Y.J., Shen, J.N., Shen, J.F. and Ma, Z.F. (2015), “State of health estimation of lithium-ion batteries: a multiscale Gaussian process regression modeling approach”, AICHE Journal, Vol. 61 No. 5, pp. 1589-1600.
Hu, X.S., Jiang, H.F., Feng, F. and Liu, B. (2020), “An enhanced multi-state estimation hierarchy for advanced lithium-ion battery management”, Applied Energy, Vol. 257, p. 114019.
Hua, Y., Cordoba-Arenas, A., Warner, N. and Rizzoni, G. (2015), “A multi time-scale state-of-charge and state-of-health estimation framework using nonlinear predictive filter for lithium-ion battery pack with passive balance control”, Journal of Power Sources, Vol. 280, pp. 293-312.
Ishizaki, R., Lin, L. and Fukui, M. (2015), “An accurate SOC estimation method for lithium-ion batteries which considers thermal variation”, Vol. 83 No. 10, pp. 582-854.
Kim, J. and Cho, B.H. (2011), “State-of-charge estimation and state-of-health prediction of a Li-ion degraded battery based on an EKF combined with a per-unit system”, IEEE Transactions on Vehicular Technology, Vol. 60 No. 9, pp. 4249-4260.
Kim, J., Lee, S. and Cho, B.H. (2012), “Complementary cooperation algorithm based on DEKF combined with pattern recognition for SOC/capacity estimation and SOH prediction”, IEEE Transactions on Power Electronics, Vol. 27 No. 1, pp. 436-451.
Lin, C., Yu, Q.Q., Xiong, R. and Wang, L.Y. (2017), “A study on the impact of open circuit voltage tests on state of charge estimation for lithium-ion batteries”, Applied Energy, Vol. 205, pp. 892-902.
Liu, D.T., Yin, X.H., Song, Y.C., Liu, W. and Peng, Y. (2018), “An on-line state of health estimation of lithium-ion battery using unscented particle filter”, 2018, IEEE Access, Vol. 6, pp. 40990-41001.
Ma, Y., Chen, Y., Zhou, X.W. and Chen, H. (2019), “Remaining useful life prediction of lithium-ion battery based on Gauss-Hermite particle filter”, IEEE Transactions on Control Systems Technology, Vol. 27 No. 4, pp. 1788-1795.
Murariu, T. and Morari, C. (2019), “Time-dependent analysis of the state-of-health for lead-acid batteries: an EIS study”, Journal of Energy Storage, Vol. 21, pp. 87-93.
Pattipati, B., Sankavaram, C. and Pattipati, K.R. (2011), “System identification and estimation framework for pivotal automotive battery management system characteristics”, IEEE Transactions on System Man and Cybernetics Part C – Applications and Reviews, Vol. 41 No. 6, pp. 869-884.
Roscher, M.A. and Sauer, D.U. (2011), “Dynamic electric behavior and open-circuit-voltage modeling of LiFePO4-based lithium ion secondary batteries”, Journal of Power Sources, Vol. 196 No. 1, pp. 331-336.
Song, S.X., Fei, C. and Xia, H.Y. (2020), “Lithium-ion battery SOH estimation based on XGBoost algorithm with accuracy correction”, Energies, Vol. 13 No. 4, p. 812.
Stroe, D.I. and Schaltz, E. (2020), “Lithium-ion battery state-of-health estimation using the incremental capacity analysis technique”, IEEE Transactions on Industry Applications, Vol. 56 No. 1, pp. 678-685.
Tong, S.J., Klein, M.P. and Park, J.W. (2015), “On-line optimization of battery open circuit voltage for improved state-of-charge and state-of-health estimation”, Journal of Power Sources, Vol. 293, pp. 416-428.
Wei, X., Mo, Y.M. and Feng, Z. (2019), “Lithium-ion battery modeling and state of charge estimation”, Integrated Ferroelectrics, Vol. 200 No. 1, pp. 59-72.
Yan, W.Z., Zhang, B., Zhao, G.Q., Tang, S.J., Niu, G.X. and Wang, X.F. (2019), “A battery management system with a Lebesgue-sampling-based extended Kalman filter”, IEEE Transactions on Industrial Electronics, Vol. 66 No. 4, pp. 3227-3236.
Yang, S.T., Ling, C., Fan, Y.Q., Yang, Y.G., Tan, X.J. and Dong, H.Y. (2019), “A review of lithium-ion Battery thermal management system strategies and the evaluate criteria”, International Journal of Electrochemical Science, Vol. 14 No. 7, pp. 6077-6107.
Ye, K.L. and Li, P.Q., “A new adaptive PSO-PID control strategy of hybrid energy storage system for electric vehicles”, Advances in Mechanical Engineering. doi: 10.1177/1687814020958574.
Ye, K.L., Li, P.Q. and Li, H. (2020), “Optimization of hybrid energy storage system control strategy for pure electric vehicle based on typical driving cycle”, Mathematical Problems in Engineering, Vol. 2020, p. 1365195.
Zhang, R.F., Xia, B.Z., Li, B.H., Cao, L.B., Lai, Y.Z., Zheng, W.W., Wang, H.W. and Wang, W. (2018), “State of the art of lithium-ion battery SOC estimation for electrical vehicles”, Energies, Vol. 11 No. 7, p. 1820, UNSP.
Zhang, X., Gao, Y.Z., Guo, B.J., Zhu, C., Zhou, X., Wang, L. and Cao, J.H. (2020), “A novel quantitative electrochemical aging model considering side reactions for lithium-ion batteries”, Electrochimica Acta, Vol. 343, p. 136070.
Zheng, F.D. (2017), Multi-time Scale State Estimation of Lithium-Ion Batteries Using Data Drive Method, Beijing Jiaotong University, (in Chinese).
Zhou, X.W. (2016), Research on SOH Estimation and RUL Prediction Methods of Lithium-Ion Battery for Electric Vehicles, Jilin University, (in Chinese).
Zou, C.F., Manzie, C., Nesic, D. and Kallapur, A.G. (2016), “Multi-time-scale observer design for state-of-charge and state-of-health of a lithium-ion battery”, Journal of Power Sources, Vol. 335, pp. 121-130.
Acknowledgements
Funding: This research was funded by the National Natural Science Foundation of China, and Natural Science Foundation of Zhejiang Province. Grant Number: 51741810, 71871078, LGG18E080005.Conflicts of Interest: The authors declare no conflict of interest.