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Lithium-ion Battery SoC Estimation with UKF and RTOS μCOS-II Platform
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 61 (2014) 468 – 471
The 6th International Conference on Applied Energy – ICAE2014
Lithium-Ion Battery SoC Estimation with UKF and RTOS μCOS-II Platform Hongwen Hea*, Hongzhou Qina, Yuanpeng Shuia, Karpenko Oleksandrb a
b
Beijing Institute of Technology, No.5 Zhongguancun South Street, Beijing, 100081, China Poltava National Technical Yuri Kondratyuk University, Pershotravneva Avenue 24, Poltava, 36011, Ukraine
Abstract To develop a battery management system for lithium-Ion batteries used in electric vehicles, the state of charge (SoC) estimation is improved with an unscented Kalman filter (UKF) and realized with the RTOS μCOS-II platform. The Kalman filters approach is broadly used for the battery SOC estimation recently. Here, we select the UKF algorithm, for which utilizes the unsented transform to solve filtering problems and is able to accurately capture the posterior mean and covariance to 3rd order of Taylor series expansion, as a result, the SoC estimation accuracy is improved with a faster convergence ability. To further evaluate the real-time performance of the SoC estimation, a battery-inloop platform is built and the SoC estimation is calculated with a RTOS μCOS-II platform. The analog acquisition, communication system and SoC estimation algorithms were programmed, the performance of the proposed SoC estimation with UKF algorithm was finally investigated. The battery management system with UKF algorithm and RTOS μCOS-II platform has good performance and can apply for electric vehicles. Keywords: electric vehicles, SoC estimation, unscented Kalman filter, Battery management system, Battery-in-the-loop
1. Introduction To solve such problems as environment pollution and energy crisis, new energy vehicles especially battery electric vehicle has become the only selection. Lithium-ion battery, for its advantages as high nominal cell voltage [1], high energy density has become a promising alternative power source of electric vehicles (EVs). It is necessary to do some research on battery management system to improve battery performance and extend its lifetime. One of the main features is state of charge (SOC) [2-3] which describes the percentage of the battery available capacity to its rated capacity. Techniques for the estimation of SOC of a battery can be categorized as direct computational methods or intelligent computational methods. Direct computational methods calculate the SOC directly based on its relationship with measurable battery parameters which would suffer from relatively poor accuracy due to accumulative errors. Intelligent computational methods include those artificial neural networks and extended Kalman filter. The artificial neural networks approach has the advantage of adaptive learning, and can cope with the battery’s nonlinear characteristics. However, it requires a large amount of data for training and the accuracy is affected significantly by the training data and training method. This study aims to address the SOC estimation issues using unscented Kalman filter (UKF) arising from system interference noise in practical application and complete the verification of the hard-in-loop
1876-6102 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of ICAE2014 doi:10.1016/j.egypro.2014.11.1150
469
Hongwen He et al. / Energy Procedia 61 (2014) 468 – 471
using RTOS.A dynamic battery model is first formulated as the basis for SOC estimation. μCOS-Ċ, which is famous for its robust and open source, is applied in the realization of the hardware. At last, related tasks including analog acquisition, communication system and SOC estimation algorithms would be programmed and the performance of the proposed UKF algorithms in SOC estimation is finally investigated. 2. Battery model Thevenin model is a widely used battery model which connects a parallel RC network in series based on the Rint model, describing the dynamic characteristics of the battery. As shown in the figure 1, R0 is an ohm resistance; Rp is a polarized resistance while the equivalent capacitance Cp is used to describe the transient response during charging and discharging. UL is used to describe the terminal voltage and Up is the voltage across Cp. Ip is the outflow current of Cp. From the Thevenin model and SoC definition, we easily have: °U L U OC U P I L Ro ® °¯U p,k exp('t / W ) u U P,k-1 1 exp('t / W ) u I L,i-1RP t
SoCt
SoC0
Fig.1.Schematic of the Thevenin
(1) (2)
1 K I L,IJ dW Ca ³0
Where W RPCP , 't denotes the sampling interval (1s in this paper). U P,k-1 is the value of U P at kth step. I L,k is the value of I L at kth step, SoCt is the present SoC , SoC is the initial value of SoC, Ca is the present maximum available capacity . K is the charge-discharge efficiency which is adopted as 100% herein. Combining the battery model and the Ah counting method, a comprehensive battery model could easily be established. Here, U , SoC are chosen as state variable while U L is the observable variable, and the state equation can be expressed as: In this model, the input Uk is the working current, X k 1 Ak X k BkU k wk and the output is the battery terminal voltage. In (3) °Y addition to the SoC, the voltage of equivalent ° k 1 Ck X k DkU k vk ° § exp('t / RP CP ) 0 · capacity u is taken into consideration as an ° Ak ¨ ¸ 0 1¹ ° © auxiliary state. The model noise is w and ° ® § RP (1-exp(-'t/RP CP )) · measurement noise is v, both w and v are B ° k ¨ ¸ K't / Ca © ¹ assumed to be mutually uncorrelated white ° ° dU oc dR0 Gaussian random processes with zero I u ] °Ck [1 dSoC dSoC ° mean, wk ~ (0, Qk ) . ¯° Dk > R0 @ ® ¯vk ~ (0, Rk ) 0
P
L
3. UKF Application in SOC Estimation UKF is proposed to solve the filtering problem in some severe nonlinear systems. Based on the idea that it is easier to approximate the probability density of the nonlinear function than the nonlinear function itself, the unscented Transform (UT) is applied in UKF, which can be described as figure 2. Also the SoC estimation process can be expressed as figure 3. 4. Experiments and analyst The experiment is performed using a battery with its actual available capacity of 25Ah and terminal voltage of 4.2V. Arbin, which has the accuracy of r0.02%FS , is used to charge and discharge, record as the standard data. In the meanwhile we design the hardware with FreescaleXF512 for signal processing, then the UKF algorithm is applied in the hardware to collect, analyze and record the data to test and verify its
470
Hongwen He et al. / Energy Procedia 61 (2014) 468 – 471
feasibility. To ensure the real-time and robustness of the whole program, μCOS-Ċ is adopted as the embedded operating system [4]. After being transplanted in XF512, we design three main task, one is Voltage and current collected every 20ms, the other is Communication with pc using can bus every 50ms,and another is Calculation the estimation using UKF every 1s.The structure of the project in codewarrior can be seen as figure 4.
Wi (m)
y
x
Yi
f ()
a n N
Px
^F ` i
ªx ¬
x a Px
Py
Wi (c)
x a Px º ¼
Fig.2. UT Transform
Fig.3. SoC estimation based on UKF
BJDC is selected to evaluate the algorithm. In this paper, ten periods of BJDC are employed to verify the accuracy of UKF.The current profile gathered by Arbin instrument during consecutive BJDC cycles is shown figure 5 while figure 6 shows the current profile collected by XF512. 50
Current(A)
0
-50
Current from Arbin
-100 0
2000
4000
6000
8000 Time(sec)
10000
12000
14000
16000
Fig. 5. Current from Arbin. 50
Current(A)
0
-50
Fig.4. The project Structure
Current from XF512
-100 0
2000
4000
6000
8000 Time(sec)
10000
12000
14000
16000
Fig.6. Current from XF512.
Figure 7 and Figure 8 describe the terminal voltage curves from Arbin and XF512. The error of the two algorithms is showed in Figure 9 from which it could be easily seen that the measurement error is similar to Gaussian white noise. As a matter of fact, the error also provides us the range of the error matrix. 4.2
4.2
Voltage from Arbin
4
Voltage from XF512 4 3.8 Voltage(V)
Voltage(V)
3.8 3.6 3.4 3.2
3.4 3.2
3 2.8 0
3.6
3
2000
4000
6000
8000 10000 Time(sec)
12000
Fig.7. Voltage from Arbin.
14000
16000
18000
2.8 0
2000
4000
6000
8000 10000 Time(sec)
12000
Figure 8. Voltage from XF512
14000
16000
18000
471
Hongwen He et al. / Energy Procedia 61 (2014) 468 – 471
For UKF application, its initial parameters are specialized as: 0.08 Voltage Error
ª0.9910 0 º A « 1 »¼ ¬ 0 C
0.04 E rro r V o lta g e (V )
> 2.8800e-005 T >1 3.8809@
B
0.06
T
8.9606e-006@
0.02 0 -0.02 -0.04 -0.06
D [0.0014]
Fig.9.Voltage Error Curve To validate the availability of UKF, an initial SoC of 0.4 was set while the battery was fully charged at the first time. Figure 10 shows the performance of UKF. It is obvious that the algorithms can solve the initial estimation inaccuracy of SoC and track the change of experimental data. The error analysis is shown in figure11. The results show that there is a noticeable error increase especially when the battery SoC is very low, this is mainly caused by the high nonlinear operating performance of battery when it is near empty. -0.08 0
6000
8000 10000 Time(sec)
12000
14000
16000
18000
SoC Error 0.05
0.8
0 SoC Error
SoC
4000
0.1
Initial SoC=0.4 Experimental data
1
2000
0.6
0.4
-0.05 -0.1 -0.15
0.2
-0.2
0 0
2000
4000
6000
8000 10000 Time(sec)
12000
14000
16000
Fig.10. SoC estimation result (Initial SoC=0.4)
-0.25 0
18000
2000
4000
6000
8000 10000 Time(sec)
12000
14000
16000
18000
Fig.11. SoC estimation error analysis(Initial SoC=0.4)
5. Conclusion In this paper, Battery Thevenin model is selected, and UKF algorithm is employed to estimate battery SoC. Compared with commonly used methods ,which are usually tested by simulation, we develop a hardware in the practical application to verify the algorithm, the results show that the nonlinear operating performance of the battery could be tracked more correctly and the SoC can regress to the true value in a short time. As an embedded operating system, μCOS-Ċ is employed based on FreescaleXF512, the development procedure and results of the whole program prove its advantages in real time and robustness. References [1]
Kennedy B, Patterson D, Camilleri S. Use of lithium-ion batteries in electric vehicles. J Power Sources 2000; 90(2):156–62.
[2]
Hongwen H, Rui X, Xiaowei Z, Fengchun S, Jinxin F. State-of-charge estimation of the lithium-ion battery using an adaptive
[3]
G. L. Plett, Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs—Part 3. State and
[4]
Mirzaee A, Salahshoor K. Fault diagnosis and accommodation of nonlinear systems based on multiple-model adaptive
extended kalman filter based on an improved Thevenin model. IEEE Trans Veh Tech 2011; 60(4):1461-9 parameter estimation. J. Power Sources, 2004; 134 (2): 277–92. unscented Kalman filter and switched MPC and H-infinity loop-shaping controller. J Process Control 2012;22(3):626–34.
ScienceDirect Energy Procedia 61 (2014) 468 – 471
The 6th International Conference on Applied Energy – ICAE2014
Lithium-Ion Battery SoC Estimation with UKF and RTOS μCOS-II Platform Hongwen Hea*, Hongzhou Qina, Yuanpeng Shuia, Karpenko Oleksandrb a
b
Beijing Institute of Technology, No.5 Zhongguancun South Street, Beijing, 100081, China Poltava National Technical Yuri Kondratyuk University, Pershotravneva Avenue 24, Poltava, 36011, Ukraine
Abstract To develop a battery management system for lithium-Ion batteries used in electric vehicles, the state of charge (SoC) estimation is improved with an unscented Kalman filter (UKF) and realized with the RTOS μCOS-II platform. The Kalman filters approach is broadly used for the battery SOC estimation recently. Here, we select the UKF algorithm, for which utilizes the unsented transform to solve filtering problems and is able to accurately capture the posterior mean and covariance to 3rd order of Taylor series expansion, as a result, the SoC estimation accuracy is improved with a faster convergence ability. To further evaluate the real-time performance of the SoC estimation, a battery-inloop platform is built and the SoC estimation is calculated with a RTOS μCOS-II platform. The analog acquisition, communication system and SoC estimation algorithms were programmed, the performance of the proposed SoC estimation with UKF algorithm was finally investigated. The battery management system with UKF algorithm and RTOS μCOS-II platform has good performance and can apply for electric vehicles. Keywords: electric vehicles, SoC estimation, unscented Kalman filter, Battery management system, Battery-in-the-loop
1. Introduction To solve such problems as environment pollution and energy crisis, new energy vehicles especially battery electric vehicle has become the only selection. Lithium-ion battery, for its advantages as high nominal cell voltage [1], high energy density has become a promising alternative power source of electric vehicles (EVs). It is necessary to do some research on battery management system to improve battery performance and extend its lifetime. One of the main features is state of charge (SOC) [2-3] which describes the percentage of the battery available capacity to its rated capacity. Techniques for the estimation of SOC of a battery can be categorized as direct computational methods or intelligent computational methods. Direct computational methods calculate the SOC directly based on its relationship with measurable battery parameters which would suffer from relatively poor accuracy due to accumulative errors. Intelligent computational methods include those artificial neural networks and extended Kalman filter. The artificial neural networks approach has the advantage of adaptive learning, and can cope with the battery’s nonlinear characteristics. However, it requires a large amount of data for training and the accuracy is affected significantly by the training data and training method. This study aims to address the SOC estimation issues using unscented Kalman filter (UKF) arising from system interference noise in practical application and complete the verification of the hard-in-loop
1876-6102 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of ICAE2014 doi:10.1016/j.egypro.2014.11.1150
469
Hongwen He et al. / Energy Procedia 61 (2014) 468 – 471
using RTOS.A dynamic battery model is first formulated as the basis for SOC estimation. μCOS-Ċ, which is famous for its robust and open source, is applied in the realization of the hardware. At last, related tasks including analog acquisition, communication system and SOC estimation algorithms would be programmed and the performance of the proposed UKF algorithms in SOC estimation is finally investigated. 2. Battery model Thevenin model is a widely used battery model which connects a parallel RC network in series based on the Rint model, describing the dynamic characteristics of the battery. As shown in the figure 1, R0 is an ohm resistance; Rp is a polarized resistance while the equivalent capacitance Cp is used to describe the transient response during charging and discharging. UL is used to describe the terminal voltage and Up is the voltage across Cp. Ip is the outflow current of Cp. From the Thevenin model and SoC definition, we easily have: °U L U OC U P I L Ro ® °¯U p,k exp('t / W ) u U P,k-1 1 exp('t / W ) u I L,i-1RP t
SoCt
SoC0
Fig.1.Schematic of the Thevenin
(1) (2)
1 K I L,IJ dW Ca ³0
Where W RPCP , 't denotes the sampling interval (1s in this paper). U P,k-1 is the value of U P at kth step. I L,k is the value of I L at kth step, SoCt is the present SoC , SoC is the initial value of SoC, Ca is the present maximum available capacity . K is the charge-discharge efficiency which is adopted as 100% herein. Combining the battery model and the Ah counting method, a comprehensive battery model could easily be established. Here, U , SoC are chosen as state variable while U L is the observable variable, and the state equation can be expressed as: In this model, the input Uk is the working current, X k 1 Ak X k BkU k wk and the output is the battery terminal voltage. In (3) °Y addition to the SoC, the voltage of equivalent ° k 1 Ck X k DkU k vk ° § exp('t / RP CP ) 0 · capacity u is taken into consideration as an ° Ak ¨ ¸ 0 1¹ ° © auxiliary state. The model noise is w and ° ® § RP (1-exp(-'t/RP CP )) · measurement noise is v, both w and v are B ° k ¨ ¸ K't / Ca © ¹ assumed to be mutually uncorrelated white ° ° dU oc dR0 Gaussian random processes with zero I u ] °Ck [1 dSoC dSoC ° mean, wk ~ (0, Qk ) . ¯° Dk > R0 @ ® ¯vk ~ (0, Rk ) 0
P
L
3. UKF Application in SOC Estimation UKF is proposed to solve the filtering problem in some severe nonlinear systems. Based on the idea that it is easier to approximate the probability density of the nonlinear function than the nonlinear function itself, the unscented Transform (UT) is applied in UKF, which can be described as figure 2. Also the SoC estimation process can be expressed as figure 3. 4. Experiments and analyst The experiment is performed using a battery with its actual available capacity of 25Ah and terminal voltage of 4.2V. Arbin, which has the accuracy of r0.02%FS , is used to charge and discharge, record as the standard data. In the meanwhile we design the hardware with FreescaleXF512 for signal processing, then the UKF algorithm is applied in the hardware to collect, analyze and record the data to test and verify its
470
Hongwen He et al. / Energy Procedia 61 (2014) 468 – 471
feasibility. To ensure the real-time and robustness of the whole program, μCOS-Ċ is adopted as the embedded operating system [4]. After being transplanted in XF512, we design three main task, one is Voltage and current collected every 20ms, the other is Communication with pc using can bus every 50ms,and another is Calculation the estimation using UKF every 1s.The structure of the project in codewarrior can be seen as figure 4.
Wi (m)
y
x
Yi
f ()
a n N
Px
^F ` i
ªx ¬
x a Px
Py
Wi (c)
x a Px º ¼
Fig.2. UT Transform
Fig.3. SoC estimation based on UKF
BJDC is selected to evaluate the algorithm. In this paper, ten periods of BJDC are employed to verify the accuracy of UKF.The current profile gathered by Arbin instrument during consecutive BJDC cycles is shown figure 5 while figure 6 shows the current profile collected by XF512. 50
Current(A)
0
-50
Current from Arbin
-100 0
2000
4000
6000
8000 Time(sec)
10000
12000
14000
16000
Fig. 5. Current from Arbin. 50
Current(A)
0
-50
Fig.4. The project Structure
Current from XF512
-100 0
2000
4000
6000
8000 Time(sec)
10000
12000
14000
16000
Fig.6. Current from XF512.
Figure 7 and Figure 8 describe the terminal voltage curves from Arbin and XF512. The error of the two algorithms is showed in Figure 9 from which it could be easily seen that the measurement error is similar to Gaussian white noise. As a matter of fact, the error also provides us the range of the error matrix. 4.2
4.2
Voltage from Arbin
4
Voltage from XF512 4 3.8 Voltage(V)
Voltage(V)
3.8 3.6 3.4 3.2
3.4 3.2
3 2.8 0
3.6
3
2000
4000
6000
8000 10000 Time(sec)
12000
Fig.7. Voltage from Arbin.
14000
16000
18000
2.8 0
2000
4000
6000
8000 10000 Time(sec)
12000
Figure 8. Voltage from XF512
14000
16000
18000
471
Hongwen He et al. / Energy Procedia 61 (2014) 468 – 471
For UKF application, its initial parameters are specialized as: 0.08 Voltage Error
ª0.9910 0 º A « 1 »¼ ¬ 0 C
0.04 E rro r V o lta g e (V )
> 2.8800e-005 T >1 3.8809@
B
0.06
T
8.9606e-006@
0.02 0 -0.02 -0.04 -0.06
D [0.0014]
Fig.9.Voltage Error Curve To validate the availability of UKF, an initial SoC of 0.4 was set while the battery was fully charged at the first time. Figure 10 shows the performance of UKF. It is obvious that the algorithms can solve the initial estimation inaccuracy of SoC and track the change of experimental data. The error analysis is shown in figure11. The results show that there is a noticeable error increase especially when the battery SoC is very low, this is mainly caused by the high nonlinear operating performance of battery when it is near empty. -0.08 0
6000
8000 10000 Time(sec)
12000
14000
16000
18000
SoC Error 0.05
0.8
0 SoC Error
SoC
4000
0.1
Initial SoC=0.4 Experimental data
1
2000
0.6
0.4
-0.05 -0.1 -0.15
0.2
-0.2
0 0
2000
4000
6000
8000 10000 Time(sec)
12000
14000
16000
Fig.10. SoC estimation result (Initial SoC=0.4)
-0.25 0
18000
2000
4000
6000
8000 10000 Time(sec)
12000
14000
16000
18000
Fig.11. SoC estimation error analysis(Initial SoC=0.4)
5. Conclusion In this paper, Battery Thevenin model is selected, and UKF algorithm is employed to estimate battery SoC. Compared with commonly used methods ,which are usually tested by simulation, we develop a hardware in the practical application to verify the algorithm, the results show that the nonlinear operating performance of the battery could be tracked more correctly and the SoC can regress to the true value in a short time. As an embedded operating system, μCOS-Ċ is employed based on FreescaleXF512, the development procedure and results of the whole program prove its advantages in real time and robustness. References [1]
Kennedy B, Patterson D, Camilleri S. Use of lithium-ion batteries in electric vehicles. J Power Sources 2000; 90(2):156–62.
[2]
Hongwen H, Rui X, Xiaowei Z, Fengchun S, Jinxin F. State-of-charge estimation of the lithium-ion battery using an adaptive
[3]
G. L. Plett, Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs—Part 3. State and
[4]
Mirzaee A, Salahshoor K. Fault diagnosis and accommodation of nonlinear systems based on multiple-model adaptive
extended kalman filter based on an improved Thevenin model. IEEE Trans Veh Tech 2011; 60(4):1461-9 parameter estimation. J. Power Sources, 2004; 134 (2): 277–92. unscented Kalman filter and switched MPC and H-infinity loop-shaping controller. J Process Control 2012;22(3):626–34.