- Email: [email protected]
Remaining useful life prediction of Lithium-ion batteries of stratospheric airship by model-based method
Microelectronics Reliability 100–101 (2019) 113400
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Remaining useful life prediction of Lithium-ion batteries of stratospheric airship by model-based method
T
⁎
Du Xiaowei, Xu Guoning , Li Zhaojie, Miao Ying, Zhao Shuai, Du Hao Academy of Opto-electronics, Chinese Academy of Sciences, 9 DengZhuangNan Road, HaiDian District, Beijing, People's Republic of China
A B S T R A C T
Lithium-ion battery has become one of the key components of energy system of stratospheric airships for its long service life, higher energy and power density. However, battery ageing always occurs during operation and leads to performance degradation and system fault which not only causes inconvenience, but also risks serious consequences such as thermal runaway or even explosion. So it is necessary for users to obtain the time left before the battery loses its operation ability. This paper uses model-based approach to estimate the remaining useful life (RUL) of the battery used in stratospheric airship. The acquisition dataset containing voltages and currents is firstly processed by subspace identification method, and then an equivalent circuit model is set up. The values of capacitances and resistances within the circuit are identified to indicate the battery's degradation in capacity and internal resistance.
1. Introduction Lithium-ion battery has been used widely in the energy system of various fields. Especially in aeronautic and aerospace engineering, the advantages such as long service life, high energy density and wide range of operating temperature make Lithium-ion battery irreplaceable for a foreseeable future. Despite the advantages mentioned above, the fatal shortcoming of low safety is exposed by several issues and accidents related to batteries occurred during recent years: batteries of laptops from Panasonic, Dell, and Sony were successively recalled for fire hazards; airplane crashes of United Airlines for the broken-out fire from Lithium-ion battery on board; Tesla EVs' fire accidents related to batteries. All these events caused public concern to the safety issue of Lithium-ion batteries and gradually influenced the development of Lithium-ion battery industry in a negative way. To ensure the safety of the batteries, BMS (battery management system) technology has made rapid progress, the functions including data acquisition, SOC (state of charge), SOH (state of health) and SOF (state of function) estimation, thermal management and equalization were developed particularly[1]. Faults of Lithium-ion batteries usually come from ageing process or abuse operation. The only variable of SOH is not sufficient to describe the life state of one cell, especially for diagnosis system[2]. The life of a Lithium-ion battery depends greatly on environmental condition and operation mode. Normal ageing process and abuse operation can both lead to degradation and faults. So it is necessary for users to understand the ageing mechanism and detect the potential deterioration before terrible accidents occur[3,4].
⁎
Corresponding author. E-mail address: [email protected] (X. Guoning).
https://doi.org/10.1016/j.microrel.2019.113400 Received 11 May 2019; Accepted 1 July 2019 Available online 23 September 2019 0026-2714/ © 2019 Elsevier Ltd. All rights reserved.
Different from mechanical or pure electrical system, Lithium-ion battery is much more complex due to its electrochemical property[5,6]. Hysteresis and inconsistency among cells make it even harder to directly extract the life symptoms. So the methods for the prediction of remaining useful life in industrial applications are not totally suitable for Lithium-ion battery[7,8]. In this paper, model-based methods are used to set up mathematical or physical models to describe degradation processes of battery, and model parameters are updated by measured data. The health indicators, the available capacity and internal resistance are used to reflect the remaining useful life of Lithium-ion battery. 2. Modelling for Lithium-ion battery 2.1. Generalized state space model For Lithium-ion batteries, the state space model can be expressed as follows:
Xg (k + 1) = Ag Xg (k ) + Bg I (k ) + wg (k ) UT (k ) = Cg Xg (k ) + Dg I (k ) + vg (k )
Q S⎤ ⎡ wg (k ) ⎞ T v (j )T ⎤ E ⎢ ⎜⎛ δkj ⎟ ( wg (k ) g )⎥ = ⎡ T ⎢ vg (j ) S R⎥ ⎣ ⎦ ⎝ ⎠ ⎣ ⎦
(1)
(2)
The input is current I, and output is the terminal voltage U.The problem of setting up the battery model can be stated as follows: Given input currents i1, i2,…is and output voltages u1, u2,…us. Find
Microelectronics Reliability 100–101 (2019) 113400
D. Xiaowei, et al.
number of main singular values of Oi, so the order is chosen to be 3. 2.2. Model with physical meaning For the 3-order battery state-space model, the output equation can be transformed as follows:
⎡ x g1 (k ) ⎤ Uo (k ) = [Cg1 Cg 2 Cg3 ]⋅⎢ x g 2 (k ) ⎥ + Dg I (k ) ⎢ ⎥ ⎢ x g3 (k ) ⎦ ⎥ ⎣
(3)
Then the output voltage can be divided into four parts of voltages:
UT 1 (k ) = Cg1 x g1 (k ); UT 2 (k ) = Cg2 x g 2 (k ); UT 3 (k ) = Cg3 x g3 (k ); UT 4 (k ) = Dg I (k );
(4)
Each voltage except UT4 is related to the state of the model. Since each state is related to the input current, it can be concluded that each voltage is the function of input current with the initialized state value. According to the data collected above, comparisons were made between the four voltages and the input current respectively. Fig. 3 shows the trends of the voltages from generalized model of a Lithiumion cell and its input current. It can be found out that voltage UT1 increases or decreases linearly with constant charging or discharging current, which is similar to the behavior of the voltage on a large capacity when it's being charged or discharged. As for voltage UT2, It can be observed that the trend of the voltage is similar to the whole charging and discharging process of the capacity. Voltage UT3 shows a sharp change at the point of the value change of current, and when the current is constant for a while, the corresponding voltage slowly goes to nearly zero, so the voltage UT3 relates to the change rate of current. Voltage UT4 is obviously proportional to the current from its equation. According to the analysis above, the four voltages' relationship with current can be simulated by the circuits composed of capacities and resistances. As Fig. 4 shows below, Model a) can be seen as a large capacitance holding the charge flowing into the battery through the current. The value of Cb indicates the ability that a battery can store the charge. Model b) and Model c) indicate the polarization process of the battery. Model d) simulates obviously the internal ohmic resistance of the battery. Then four battery models with circuit parameters can be set up. The models were discretized and separated into four parts corresponding to the former mentioned voltages, as shown by Eqs. (5)-(8). Tc indicates the sampling period of the system.
Fig. 1. Flow chart of battery model set-up by subspace identification method.
an appropriate order n, and the system matrices, Ag, Bg, Cg, Dg and Q,R,S. Subspace identification method (SIM) is used to solve the problem above. It's a novel time domain identification method, which directly uses operational response to identify the system model by linear algebraic manipulations such as QR-factorization and singular value decomposition. By using this method, models for Li-on batteries can be set up directly from the data in real charge/discharge conditions. The procedure of the method is shown in Fig. 1. A Lithium-ion battery cell was tested in a standard operating condition, and the data from the test was used to set up the model by the method above. Fig. 2 shows the contrast between output voltage of the model and measured voltage. According to the method, the order of the model is decided by the
UCb (k ) = UCb (k − 1) +
Tc ⋅Iin (k ) Cb
Tc ⎞ T I (k ) UC p (k ) = ⎛1 − ⋅UC p (k − 1) + c in RPC CP ⎠ Cp ⎝ ⎜
(5)
⎟
(6)
k−1
R T ULp (k ) = ⎛‐ PL c ⎞⋅ ∑ ULp (i) + RPL Iin (k ) ⎝ LP ⎠ i = 0
(7)
Uohm (k ) = Rohm⋅Iin (k )
(8)
⎜
⎟
To identify the parameters in the equations above, least square method was adopted. Voltages UT1, UT2, UT3 and UT4 generated from subspace method are used for the output of the corresponding discretized model. So the parameters can be identified separately by the least square method. The complexity of calculations can be reduced and it's flexible to choose the model parameters to be identified according to demands. 3. Life determination based on battery model Fig. 2. Contrast of model voltage and measured voltage.
Nowadays, there are mainly two kinds of indicators for RUL, one is 2
Microelectronics Reliability 100–101 (2019) 113400
D. Xiaowei, et al.
Fig. 3. Trend of voltages and current.
+
Iin +
UCb
Iin
UCp
3.1. Internal resistance
−
In the equivalent circuit model set up previously, among the components Rohm, RPC, and RPL, the value of Rohm is ten times bigger than RPC, and the value of RPL is the smallest and near to zero. So the internal resistance of the battery is mainly contributed from Rohm. As Fig. 5 shows, a battery module, has been tested in a stratospheric airship for more than one year, and then drawn back for life test. The data from the test was applied to set up the model with the method above and the value of Rohm was 34.2mΩ, compared with that of the same module during its delivery test, 29.3 mΩ, there was a remarkable increase.
CP
Cb −
RPC
a)Model - UT1
b) Model - UT2
3.2. The available capacity
+ ULp − Lp Iin
+
Uohm
The decrease of the available capacity can be considered as the lack of the ability to hold the charge, and among the electrical components, capacitance usually indicates the storage of charge. Thus, considering the structure of the circuit model, the value of component Cb, can be inferred as the ability to hold the charge. A cell with the normal capacity of 3 Ampere-Hours was chosen and each of the cells with different life cycles is tested by variable operating conditions including charging and discharging processes. By extracting the dataset of currents and voltages, the value of Cb was identified for the corresponding life-cycled cell. And also the available capacity was acquired by a
−
Iin RPL c) Model - UT3
Rohm d) Model - UT4
Fig. 4. Circuit models for voltage components.
the ability of a cell/battery to perform a particular discharge (or charge) function at an instantaneous moment in the charge-dischargestand cycle regime, and the other is the ability of that battery to repeatedly provide its rated capacity over time. So the prediction of RUL is mainly concerned with the internal resistance and the available capacity in a battery.
Fig. 5. Part of battery pack from a stratospheric airship. 3
Microelectronics Reliability 100–101 (2019) 113400
D. Xiaowei, et al.
Table 1 Estimated values of remaining useful life and uncertainties for Lithium-ion battery (unit: cycle). Battery module
Estimated RUL
Actual RUL
Absolute prediction error
1 2 3 4 5
84 43 104 175 205
91 46 109 181 210
7 3 5 6 5
1) 2) 3) 4)
The available capacity and internal resistance can be calibrated by the last step within each cycle. And life cycle test is not terminated until the capacity is reduced by 20%. After each cycle, the real capacity and internal resistance can be acquired, and also the corresponding number of cycles can be recorded. Therefore an interpolation table can be set up for internal resistance and the available capacity, each value with a corresponding number of cycles. Then RUL can be predicted by interpolation method after the internal resistance and the available capacity are acquired by methods introduced in 3.1 and 3.2. Five battery modules used in the stratospheric airship were selected and different durations of operation conditions were imposed on these modules. RUL of each battery module was estimated by the method above. The real RUL was acquired by carrying the life cycle test. The results show that the method is effective in predicting remaining useful life of Lithium-ion batteries (see Table 1).
Fig. 6. Relationship between available capacity and Cb.
regime of C/3 discharging current to be empty after the cell is charged to be full of charge. As Fig. 6 shows, the available capacity is nearly linear to the variation of the value of Cb. Based on the above analysis, the available capacity Cavail is highly linear with the value of Cb: (9)
Cavail = A*Cb + B Values of A and B can be acquired by least square method. 3.3. RUL prediction method
The energy system in a stratospheric airship is usually composed of several solar battery components, a Lithium-ion battery pack, and a power control unit. As for the Lithium-ion battery, modes of charge and discharge greatly depend on the solar intensity and load demands. In stratosphere, the solar intensity and wind speed/direction relatively follow the same pattern within a day. Therefore the charging and discharging process of the battery can be seen as invariable from day to day. As Fig. 7 shows, a regime of charging and discharging current is designed to simulate the real condition within 24 h. So a cycling life test can be carried out by applying the regime mentioned above. Since after each regime being carried out, the charge within the battery is reduced by 40%.So each life cycle test is designed to be composed of four steps:
4. Conclusions A generalized 3-order model is firstly set up by subspace identification method, directly using the dataset of currents and voltages. By analyzing the relationship between the current and each element of the output voltage of the model, the circuit models with resistances, capacitances and inductors are built to simulate the corresponding relationship. Among all the models, ohmic internal resistance of the battery is easily identified by the ohmic resistance model, and the model of a large capacitance is used to indicate the ability of the battery to store the charge. Then the available capacity is found to be linear to the value of the large capacitance Cb and can be easily calculated. After the value of internal resistance and the available capacity are acquired, the remaining useful life can be predicted through interpolation tables of both. The data-driven method is firstly used to extract useful information, including the order of the model and relationships between current and the voltage components. Model with physical meaning can be wellfounded based on the above information and health indicators, internal resistance and the available capacity are identified to predict RUL.
0.06 0.04 Rat e o f Cu r r en t (C)
Start with SOC of 100%. The regime is carried out and SOC is reduced by 40%. Discharge until the voltage reaches a lower limit. Charge until the voltage reaches an upper limit.
0.02 0.00
Declaration of Competing Interest -0.02
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
-0.04 0
5
10
15
20
25
Acknowledgements
Time (Hour)
This work is supported by the Scientific Experimental System in Near Space of Chinese Academy of Sciences (Grant No. XDA17000000).
Fig. 7. Rate of charge/discharge current during a day. 4
Microelectronics Reliability 100–101 (2019) 113400
D. Xiaowei, et al.
References
Brownian motion with an adaptive drif, Microelectron. Reliab. 51 (2011) 285–293. [5] H. Li, D. Pan, C.L.P. Chen, Reliability modeling and life estimation using an expectation maximization based wiener degradation model for momentum wheels, IEEE Trans. Cybern. 45 (2015) 955–963. [6] B. Saha, K. Goebel, S. Poll, and J. Christophersen. Prognostics methods for battery health monitoring using a Bayesian framework. IEEE Trans. Instrum. Meas..v58 (2009) 291–296. [7] S.J. Tang, C.Q. Yu, X. Wang, X.S. Guo, X.S. Si, Remaining useful life prediction of lithium-ion batteries based on the Wiener process with measurement error, Energies 7 (2014) 520–547. [8] X. Wang, N. Balakrishnan, B. Guo, Residual life estimation based on a generalized Wiener degradation process, Reliab. Eng. Syst. Saf. 124 (2014) 13–23.
[1] Bin Yu, Tao Zhang, Tianyu Liu, and Lei Yao. Reliability evaluation and in-orbit residual life prediction for satellite lithium-ion batteries. Math. Probl. Eng.. Vol. 2018, Article ID 5918068, 12 pages, 2018. [2] H. Dong, X. Jin b, Y. Lou b, C. Wang, Lithium-ion battery state of health monitoring and remaining usefullife prediction based on support vector regression-particle filter, J. Power Sources 271 (2014) 114–123. [3] D. Wang, Q. Miao, M. Pecht, Prognostics of lithium-ion batteries based on relevance vectors and a conditional three-parameter capacity degradation model, J. Power Sources 239 (2013) 253–264. [4] W. Wang, M. Carr, W. Xu, K. Kobbacy, A model for residuallife prediction based on
5
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Remaining useful life prediction of Lithium-ion batteries of stratospheric airship by model-based method
T
⁎
Du Xiaowei, Xu Guoning , Li Zhaojie, Miao Ying, Zhao Shuai, Du Hao Academy of Opto-electronics, Chinese Academy of Sciences, 9 DengZhuangNan Road, HaiDian District, Beijing, People's Republic of China
A B S T R A C T
Lithium-ion battery has become one of the key components of energy system of stratospheric airships for its long service life, higher energy and power density. However, battery ageing always occurs during operation and leads to performance degradation and system fault which not only causes inconvenience, but also risks serious consequences such as thermal runaway or even explosion. So it is necessary for users to obtain the time left before the battery loses its operation ability. This paper uses model-based approach to estimate the remaining useful life (RUL) of the battery used in stratospheric airship. The acquisition dataset containing voltages and currents is firstly processed by subspace identification method, and then an equivalent circuit model is set up. The values of capacitances and resistances within the circuit are identified to indicate the battery's degradation in capacity and internal resistance.
1. Introduction Lithium-ion battery has been used widely in the energy system of various fields. Especially in aeronautic and aerospace engineering, the advantages such as long service life, high energy density and wide range of operating temperature make Lithium-ion battery irreplaceable for a foreseeable future. Despite the advantages mentioned above, the fatal shortcoming of low safety is exposed by several issues and accidents related to batteries occurred during recent years: batteries of laptops from Panasonic, Dell, and Sony were successively recalled for fire hazards; airplane crashes of United Airlines for the broken-out fire from Lithium-ion battery on board; Tesla EVs' fire accidents related to batteries. All these events caused public concern to the safety issue of Lithium-ion batteries and gradually influenced the development of Lithium-ion battery industry in a negative way. To ensure the safety of the batteries, BMS (battery management system) technology has made rapid progress, the functions including data acquisition, SOC (state of charge), SOH (state of health) and SOF (state of function) estimation, thermal management and equalization were developed particularly[1]. Faults of Lithium-ion batteries usually come from ageing process or abuse operation. The only variable of SOH is not sufficient to describe the life state of one cell, especially for diagnosis system[2]. The life of a Lithium-ion battery depends greatly on environmental condition and operation mode. Normal ageing process and abuse operation can both lead to degradation and faults. So it is necessary for users to understand the ageing mechanism and detect the potential deterioration before terrible accidents occur[3,4].
⁎
Corresponding author. E-mail address: [email protected] (X. Guoning).
https://doi.org/10.1016/j.microrel.2019.113400 Received 11 May 2019; Accepted 1 July 2019 Available online 23 September 2019 0026-2714/ © 2019 Elsevier Ltd. All rights reserved.
Different from mechanical or pure electrical system, Lithium-ion battery is much more complex due to its electrochemical property[5,6]. Hysteresis and inconsistency among cells make it even harder to directly extract the life symptoms. So the methods for the prediction of remaining useful life in industrial applications are not totally suitable for Lithium-ion battery[7,8]. In this paper, model-based methods are used to set up mathematical or physical models to describe degradation processes of battery, and model parameters are updated by measured data. The health indicators, the available capacity and internal resistance are used to reflect the remaining useful life of Lithium-ion battery. 2. Modelling for Lithium-ion battery 2.1. Generalized state space model For Lithium-ion batteries, the state space model can be expressed as follows:
Xg (k + 1) = Ag Xg (k ) + Bg I (k ) + wg (k ) UT (k ) = Cg Xg (k ) + Dg I (k ) + vg (k )
Q S⎤ ⎡ wg (k ) ⎞ T v (j )T ⎤ E ⎢ ⎜⎛ δkj ⎟ ( wg (k ) g )⎥ = ⎡ T ⎢ vg (j ) S R⎥ ⎣ ⎦ ⎝ ⎠ ⎣ ⎦
(1)
(2)
The input is current I, and output is the terminal voltage U.The problem of setting up the battery model can be stated as follows: Given input currents i1, i2,…is and output voltages u1, u2,…us. Find
Microelectronics Reliability 100–101 (2019) 113400
D. Xiaowei, et al.
number of main singular values of Oi, so the order is chosen to be 3. 2.2. Model with physical meaning For the 3-order battery state-space model, the output equation can be transformed as follows:
⎡ x g1 (k ) ⎤ Uo (k ) = [Cg1 Cg 2 Cg3 ]⋅⎢ x g 2 (k ) ⎥ + Dg I (k ) ⎢ ⎥ ⎢ x g3 (k ) ⎦ ⎥ ⎣
(3)
Then the output voltage can be divided into four parts of voltages:
UT 1 (k ) = Cg1 x g1 (k ); UT 2 (k ) = Cg2 x g 2 (k ); UT 3 (k ) = Cg3 x g3 (k ); UT 4 (k ) = Dg I (k );
(4)
Each voltage except UT4 is related to the state of the model. Since each state is related to the input current, it can be concluded that each voltage is the function of input current with the initialized state value. According to the data collected above, comparisons were made between the four voltages and the input current respectively. Fig. 3 shows the trends of the voltages from generalized model of a Lithiumion cell and its input current. It can be found out that voltage UT1 increases or decreases linearly with constant charging or discharging current, which is similar to the behavior of the voltage on a large capacity when it's being charged or discharged. As for voltage UT2, It can be observed that the trend of the voltage is similar to the whole charging and discharging process of the capacity. Voltage UT3 shows a sharp change at the point of the value change of current, and when the current is constant for a while, the corresponding voltage slowly goes to nearly zero, so the voltage UT3 relates to the change rate of current. Voltage UT4 is obviously proportional to the current from its equation. According to the analysis above, the four voltages' relationship with current can be simulated by the circuits composed of capacities and resistances. As Fig. 4 shows below, Model a) can be seen as a large capacitance holding the charge flowing into the battery through the current. The value of Cb indicates the ability that a battery can store the charge. Model b) and Model c) indicate the polarization process of the battery. Model d) simulates obviously the internal ohmic resistance of the battery. Then four battery models with circuit parameters can be set up. The models were discretized and separated into four parts corresponding to the former mentioned voltages, as shown by Eqs. (5)-(8). Tc indicates the sampling period of the system.
Fig. 1. Flow chart of battery model set-up by subspace identification method.
an appropriate order n, and the system matrices, Ag, Bg, Cg, Dg and Q,R,S. Subspace identification method (SIM) is used to solve the problem above. It's a novel time domain identification method, which directly uses operational response to identify the system model by linear algebraic manipulations such as QR-factorization and singular value decomposition. By using this method, models for Li-on batteries can be set up directly from the data in real charge/discharge conditions. The procedure of the method is shown in Fig. 1. A Lithium-ion battery cell was tested in a standard operating condition, and the data from the test was used to set up the model by the method above. Fig. 2 shows the contrast between output voltage of the model and measured voltage. According to the method, the order of the model is decided by the
UCb (k ) = UCb (k − 1) +
Tc ⋅Iin (k ) Cb
Tc ⎞ T I (k ) UC p (k ) = ⎛1 − ⋅UC p (k − 1) + c in RPC CP ⎠ Cp ⎝ ⎜
(5)
⎟
(6)
k−1
R T ULp (k ) = ⎛‐ PL c ⎞⋅ ∑ ULp (i) + RPL Iin (k ) ⎝ LP ⎠ i = 0
(7)
Uohm (k ) = Rohm⋅Iin (k )
(8)
⎜
⎟
To identify the parameters in the equations above, least square method was adopted. Voltages UT1, UT2, UT3 and UT4 generated from subspace method are used for the output of the corresponding discretized model. So the parameters can be identified separately by the least square method. The complexity of calculations can be reduced and it's flexible to choose the model parameters to be identified according to demands. 3. Life determination based on battery model Fig. 2. Contrast of model voltage and measured voltage.
Nowadays, there are mainly two kinds of indicators for RUL, one is 2
Microelectronics Reliability 100–101 (2019) 113400
D. Xiaowei, et al.
Fig. 3. Trend of voltages and current.
+
Iin +
UCb
Iin
UCp
3.1. Internal resistance
−
In the equivalent circuit model set up previously, among the components Rohm, RPC, and RPL, the value of Rohm is ten times bigger than RPC, and the value of RPL is the smallest and near to zero. So the internal resistance of the battery is mainly contributed from Rohm. As Fig. 5 shows, a battery module, has been tested in a stratospheric airship for more than one year, and then drawn back for life test. The data from the test was applied to set up the model with the method above and the value of Rohm was 34.2mΩ, compared with that of the same module during its delivery test, 29.3 mΩ, there was a remarkable increase.
CP
Cb −
RPC
a)Model - UT1
b) Model - UT2
3.2. The available capacity
+ ULp − Lp Iin
+
Uohm
The decrease of the available capacity can be considered as the lack of the ability to hold the charge, and among the electrical components, capacitance usually indicates the storage of charge. Thus, considering the structure of the circuit model, the value of component Cb, can be inferred as the ability to hold the charge. A cell with the normal capacity of 3 Ampere-Hours was chosen and each of the cells with different life cycles is tested by variable operating conditions including charging and discharging processes. By extracting the dataset of currents and voltages, the value of Cb was identified for the corresponding life-cycled cell. And also the available capacity was acquired by a
−
Iin RPL c) Model - UT3
Rohm d) Model - UT4
Fig. 4. Circuit models for voltage components.
the ability of a cell/battery to perform a particular discharge (or charge) function at an instantaneous moment in the charge-dischargestand cycle regime, and the other is the ability of that battery to repeatedly provide its rated capacity over time. So the prediction of RUL is mainly concerned with the internal resistance and the available capacity in a battery.
Fig. 5. Part of battery pack from a stratospheric airship. 3
Microelectronics Reliability 100–101 (2019) 113400
D. Xiaowei, et al.
Table 1 Estimated values of remaining useful life and uncertainties for Lithium-ion battery (unit: cycle). Battery module
Estimated RUL
Actual RUL
Absolute prediction error
1 2 3 4 5
84 43 104 175 205
91 46 109 181 210
7 3 5 6 5
1) 2) 3) 4)
The available capacity and internal resistance can be calibrated by the last step within each cycle. And life cycle test is not terminated until the capacity is reduced by 20%. After each cycle, the real capacity and internal resistance can be acquired, and also the corresponding number of cycles can be recorded. Therefore an interpolation table can be set up for internal resistance and the available capacity, each value with a corresponding number of cycles. Then RUL can be predicted by interpolation method after the internal resistance and the available capacity are acquired by methods introduced in 3.1 and 3.2. Five battery modules used in the stratospheric airship were selected and different durations of operation conditions were imposed on these modules. RUL of each battery module was estimated by the method above. The real RUL was acquired by carrying the life cycle test. The results show that the method is effective in predicting remaining useful life of Lithium-ion batteries (see Table 1).
Fig. 6. Relationship between available capacity and Cb.
regime of C/3 discharging current to be empty after the cell is charged to be full of charge. As Fig. 6 shows, the available capacity is nearly linear to the variation of the value of Cb. Based on the above analysis, the available capacity Cavail is highly linear with the value of Cb: (9)
Cavail = A*Cb + B Values of A and B can be acquired by least square method. 3.3. RUL prediction method
The energy system in a stratospheric airship is usually composed of several solar battery components, a Lithium-ion battery pack, and a power control unit. As for the Lithium-ion battery, modes of charge and discharge greatly depend on the solar intensity and load demands. In stratosphere, the solar intensity and wind speed/direction relatively follow the same pattern within a day. Therefore the charging and discharging process of the battery can be seen as invariable from day to day. As Fig. 7 shows, a regime of charging and discharging current is designed to simulate the real condition within 24 h. So a cycling life test can be carried out by applying the regime mentioned above. Since after each regime being carried out, the charge within the battery is reduced by 40%.So each life cycle test is designed to be composed of four steps:
4. Conclusions A generalized 3-order model is firstly set up by subspace identification method, directly using the dataset of currents and voltages. By analyzing the relationship between the current and each element of the output voltage of the model, the circuit models with resistances, capacitances and inductors are built to simulate the corresponding relationship. Among all the models, ohmic internal resistance of the battery is easily identified by the ohmic resistance model, and the model of a large capacitance is used to indicate the ability of the battery to store the charge. Then the available capacity is found to be linear to the value of the large capacitance Cb and can be easily calculated. After the value of internal resistance and the available capacity are acquired, the remaining useful life can be predicted through interpolation tables of both. The data-driven method is firstly used to extract useful information, including the order of the model and relationships between current and the voltage components. Model with physical meaning can be wellfounded based on the above information and health indicators, internal resistance and the available capacity are identified to predict RUL.
0.06 0.04 Rat e o f Cu r r en t (C)
Start with SOC of 100%. The regime is carried out and SOC is reduced by 40%. Discharge until the voltage reaches a lower limit. Charge until the voltage reaches an upper limit.
0.02 0.00
Declaration of Competing Interest -0.02
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
-0.04 0
5
10
15
20
25
Acknowledgements
Time (Hour)
This work is supported by the Scientific Experimental System in Near Space of Chinese Academy of Sciences (Grant No. XDA17000000).
Fig. 7. Rate of charge/discharge current during a day. 4
Microelectronics Reliability 100–101 (2019) 113400
D. Xiaowei, et al.
References
Brownian motion with an adaptive drif, Microelectron. Reliab. 51 (2011) 285–293. [5] H. Li, D. Pan, C.L.P. Chen, Reliability modeling and life estimation using an expectation maximization based wiener degradation model for momentum wheels, IEEE Trans. Cybern. 45 (2015) 955–963. [6] B. Saha, K. Goebel, S. Poll, and J. Christophersen. Prognostics methods for battery health monitoring using a Bayesian framework. IEEE Trans. Instrum. Meas..v58 (2009) 291–296. [7] S.J. Tang, C.Q. Yu, X. Wang, X.S. Guo, X.S. Si, Remaining useful life prediction of lithium-ion batteries based on the Wiener process with measurement error, Energies 7 (2014) 520–547. [8] X. Wang, N. Balakrishnan, B. Guo, Residual life estimation based on a generalized Wiener degradation process, Reliab. Eng. Syst. Saf. 124 (2014) 13–23.
[1] Bin Yu, Tao Zhang, Tianyu Liu, and Lei Yao. Reliability evaluation and in-orbit residual life prediction for satellite lithium-ion batteries. Math. Probl. Eng.. Vol. 2018, Article ID 5918068, 12 pages, 2018. [2] H. Dong, X. Jin b, Y. Lou b, C. Wang, Lithium-ion battery state of health monitoring and remaining usefullife prediction based on support vector regression-particle filter, J. Power Sources 271 (2014) 114–123. [3] D. Wang, Q. Miao, M. Pecht, Prognostics of lithium-ion batteries based on relevance vectors and a conditional three-parameter capacity degradation model, J. Power Sources 239 (2013) 253–264. [4] W. Wang, M. Carr, W. Xu, K. Kobbacy, A model for residuallife prediction based on
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