- Email: [email protected]
Study on Battery Pack Consistency Evolutions during Electric Vehicle Operation with Statistical Method
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 105 (2017) 3551 – 3556
The 8th International Conference on Applied Energy – ICAE2016
Study on battery pack consistency evolutions during electric vehicle operation with statistical method Caiping Zhanga,b,*, Gong Chenga,b, Qun Juc,Weige Zhanga,b, Jiuchun Jianga,b, Linjing Zhanga,b a
National Active Distribution Network Technology Research Center (NANTEC), Beijing Jiaotong University, Beijing, 100044, China b Collaborative Innovation Center of Electric Vehicles in Beijing, Beijing Jiaotong University, Beijing 100044, China c Lithium Battery Product Quality Supervision and Inspection Center, Zaozhuang, Shandong Province,China
Abstract: The consistency among lithium-ion battery pack is an important factor affecting their performance. In order to investigate the battery pack consistency evolutions and influencing factors from statistics point of view, long-term battery data of two trolley buses are collected. Two parameters including the internal resistance and open-circuit voltage (OCV) are chosen to describe battery pack consistency in the study. The mathematical relationship between the battery pack OCV standard deviation after a period time and the intimal standard deviation with polynomial model is established. It is proved that the model error is within 6%. It is demonstrated that battery temperature has the greatest impact on the internal resistance consistency of the battery pack through correlation analysis. The initial SOC inconsistency and temperature of the battery are two key factors affecting the battery pack consistency based on the operation data, providing a foundation for battery consistency improvement.
© Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license © 2017 2016 The The Authors. Authors. Published Published by by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or under responsibility of ICAE of the 8th International Conference on Applied Energy. Peer-review underpeer-review responsibility of the scientific committee Keywords: Lithium-ion battery pack, consistency, modeling, correlation analysis
1. Introduction With the rapid development of electric vehicles, lithium-ion batteries are increasingly being used in automotive energy source. Since the batteries with good manufacturing start to show consistency after being used for a period of time, further research has been done on consistency caused by increasing usage time of electric vehicles on an international scale. In the long-term charge-discharge process, the differences among the individual cells of the charge and discharge capacity, self-discharge rate, degradation rates in the battery pack will lead to increasingly large gap between the available capacities of each cells [1-4], battery packs makes inconsistencies become an important factor affecting battery performance [5]. The consistency of OCV is one of the most intuitionistic performances of battery packs inconsistency. The standard deviations and range is mostly provided as a parameter representing the dynamic characteristic. Another intuitionistic performance is the resistance or impedance, which is analyzed through electrochemical impedance spectroscopy (EIS). Current research on battery consistency is mostly based on the laboratory experimental data. However, in the actual vehicle running condition data accuracy, sampling frequency and the experimental conditions is limited, which is not fully consistent with. Through long-term tracking of the data, we discussed the statistical laws and influencing factors of two kinds of inconsistency in battery pack, including the open circuit voltage inconsistency and the resistance consistency, which describe the consistency from aspects of battery thermodynamics and kinetic dynamics, *Corresponding author. Tel.: +86-10-51683907; fax: +86-10-51683907. E-mail address: [email protected].
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy. doi:10.1016/j.egypro.2017.03.816
3552
Caiping Zhang et al. / Energy Procedia 105 (2017) 3551 – 3556
respectively. Effectively classifying and quantifying inconsistency is helpful for analyzing the causes, effects and changes in characteristics. The remainder of this paper is organized as follows. Section II describes two definition of the inconsistency selected for study in this paper, which is inconsistency of OCV and resistance. The distribution and variation statistics are discussed in section III. A new model structure is introduced that a quantic polynomial system is acceptable for the standard deviation of OCV change models. A highly negative relationship is proved between temperature and standard deviation of the resistance, compared to the cumulative capacitance. Finally, Section IV concludes with a summary of the main findings of this paper and a highlight of related open issues [6-9]. 2. Evaluation parameters of the battery pack inconsistency The inconsistency of battery pack means inconsistent performance indicators exhibited in the group consisting of batteries. These performances include the available capacity, the Ohmic resistance and polarization resistance, polarization capacitance, temperature characteristics and the recession velocity, etc. These differences in operation will be unified shows in different output parameters [6]. Taking into account the high error rate and lower accuracy of the actual vehicle data, in the study, the open-circuit voltage and the internal resistance of the battery pack are chosen as the evaluation parameters of inconsistency. 2.1 The definition of the inconsistency of the OCV After standing for a whole night, the polarization voltage of battery pack in electric vehicles is fading. The battery management system (BMS) will record the open-circuit voltage of each cell before EV bus start at the next day. The OCV standard deviation of the battery pack, as the inconsistency coefficient on homeostasis parameter characteristics, excludes the impact of current and temperature field caused by the difference. It is an important factor of inconsistency of the pack, but also belong to reversible inconsistent, which can be used as an important reference for improved battery balancing strategy [7-9]. 2.2 The definition of the inconsistency of resistance Due to the different production process, decay rates and temperatures of the cells in the pack, the resistance exhibit differences. When the current through, it will cause greater standard deviation of voltage and greater difference in temperature field. Thereby further increase the inconsistency of the battery pack. The definition of resistance in this article is the resistance derived from the first-order RC model. Identify each piece of the battery parameters, the standard deviation of internal resistance of the battery pack can be calculated. Since disassembly the battery pack is difficult, resistance is defined as the irreversible part of the inconsistency [3,10-12]. In this paper the experimental data is the usage data for up to 7 months of battery packs in two electric trolley buses (text named Bus A and Bus B). It’s pure electric vehicles, but there are pantograph as an external power supply in some sections during operation, which can running and charging in the meantime. So the using conditions is closer to hybrid vehicles, high-current charge and discharge are mixed during running. The battery pack is connected with 3 NMC (LiNixMnyCozO2) batteries in parallel and 104 in series, packed into four battery packs (named group 1, Group 2, Group 3 and Group 4). Initial total capacity is 105Ah, capacity of each cells is 35Ah 3. The inconsistent parameter distribution and variation statistics 3.1 Analysis of the statistical regularities of the open circuit voltage 3.1.1 Analysis of the open circuit voltage distribution Single cell voltage in the battery pack is different. Its distribution is more close to normal. To determine the standard deviation as the inconsistency coefficient of open circuit voltage is rational. This paper tests the significant of normal distribution of data with the Kolmogorov–Smirnov test. Under normal circumstances, when the P value is greater than 0.05, the assumption that the data obey a normal distribution is proved. We verify the normal distribution of the open circuit voltage in Group 1 Bus A with the Kolmogorov–Smirnov test. The P value distribution is shown in Figure 1. The left y-axis is the frequency of P value occurrence. The right is the percentage of frequency of P value occurrence cumulative from small to large. There are only two points of P value smaller than 0.05 in the group, which doesn't coincided with normal distribution, accounting for 1.4% of the overall
3553
Caiping Zhang et al. / Energy Procedia 105 (2017) 3551 – 3556
20
Frequency of occurrence
18
Frequency of occurrence Cumulative Percentage
16
100 80
14 12
60
10 8
40
6 4
20
2 0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cumulative Percentageͧ%ͨ
proportion. Considering the actual operation of the BMS data often appear errors and instability, a small percentage of error is acceptable. The statistical results of the Kolmogorov–Smirnov test on daily open-circuit voltage in eight groups of two vehicles battery packs is shown in Table 1. Although the Bus B running at the similar times with Bus A, but the open circuit voltage failed to stabilize the recording of each day before start. So the effective open circuit voltage data is only half of the Bus A. Since the effective point average distribute in the entire time is more than one hundred days, the Statistical inconsistent of data changes with the continued using is still valid.
0
Statistical distribution of P value in Group 1 Bus A
Figure 1.Statistical distribution of P value texted by K-S with daily open circuit voltage Table 1.The proportion of open-circuit voltage accorded with normal distribution in each group Number of valid statistics
Number of abnormal distribution
percentage of abnormal distribution
Group 1 Bus A
138
2
98.6%
Group 2 Bus A
138
0
100%
Group 3 Bus A
138
1
99.3%
Group 4 Bus A
138
0
100%
Group 1 Bus B
61
0
100%
Group 2 Bus B
61
0
100%
Group 3 Bus B
61
0
100%
Group 4 Bus B
61
0
100%
3.1.2 Standard deviation of open circuit voltage variation analysis and modeling Up to the current study two trolley buses have being used for 160 days. We calculate the standard deviation of open circuit voltage of battery packs in two buses each day. Then we extract voltage and current data about three minutes under predetermined conditions, identify the parameters and calculate the standard deviation of internal resistance of the cells in each group. As the result shown in Fig.2 and Fig.3.Since the trolley bus daily usage is not the same, there may be a few days to repair the bus without using. Therefore the abscissa is the cumulative power of battery to indicate the status of the battery usage. The four groups of batteries in the same bus connect in series, which experience the same current conditions. Difference in manufacture, installation, temperature and vibration would cause the inconsistency of battery pack. And the two buses run on the same bus line, so the environmental temperature and the daily usage time in normal operation is substantially the same. It is clearly shown in Figure 2 that the variation tendency of standard deviation of OCV is closely, and the value is different. We evaluate the standard deviation of OCV in 4 battery groups in each Bus. Because two packs of data are not enough for accurate results evaluated by regression analysis. In this paper, the standard deviation of 8 groups of batteries in two buses are used to evaluate mathematical models, and the one of two packs of batteries in each buses are used to compute the model error. By means of the nonlinear regression analysis for a mathematical model, the equation of standard deviation before used and after using at different cumulative capacitance is given as follow.
Caiping Zhang et al. / Energy Procedia 105 (2017) 3551 – 3556
0.008
Standard Deviation/V
Standard Deviation/V
3554
0.007
0.006
0.005
0.004
Bus B
0.003 0
10000
20000
30000
40000
50000
60000
0.008
0.007
0.006
0.005
0.004
0.003 -10000
Cumulative Capacitance/Ah
Bus A 0
10000 20000 30000 40000 50000 60000 70000
Cumulative Capacitance/Ah
(a)
(b)
Figure 2.Standard deviation of open circuit voltage curve in different bus (a) Bus A; (b) Bus B
V 27584Ah -5.28*1011 * V 05 +1.18*1010 *V 04 -1.03*108 *V 03 +4.42*105 *V 02 -921.56*V 0 +0.7562 V 36423Ah -2.84*1011 * V 05 +6.13*109 *V 04 -5.17*107 *V 03 +2.12*105 *V 02 -423.81*V 0 +0.3355 V 46263Ah -9.61*1010 * V 05 +1.99*109 *V 04 -1.60*107 *V 03 +6.12*104 *V 02 -111.50*V 0 +0.0821
(1)
V 57059Ah -1.97*10 * V +4.27*10 *V -3.60*10 *V +1.47*10 *V -288.99*V 0 +0.2260 11
5 0
9
4 0
7
3 0
5
2 0
Where σ0 is the initial standard deviation of OCV, σxAh is the standard deviation when the cumulative capacitance is xAh. We use the data of battery pack for validation of the model. The initial standard deviation of OCV in Bus A is 0.00518V, and 0.00394V in Bus B. The equations of error calculation is (Simulation value-Actual value)/Actual value*100%.The result is shown as follow, which shows that a quantic polynomial system is acceptable for the standard deviation of OCV change models. Table 2. Prediction of standard deviation model error Cumulative capacitance /Ah
Bus A Actual value
Simulation value
Error
Bus B Actual value
Simulation value
Error
27584
0.00683
0.00657
-3.89%
0.00685
0.00657
-4.14%
36423
0.00707
0.00744
5.20%
0.00759
0.00744
-2.01%
46263
0.00698
0.00736
5.46%
0.00723
0.00736
1.87%
57059
0.00712
0.00749
5.25%
0.00747
0.00749
0.21%
3.2 Analysis of the statistical regularities of resistance Resistance is an important parameter to reflect the performance of the battery itself. Its value is reflected not only by the initial state of the batteries and historical recession, but also by the statuses when measuring, like current, SOC and temperature. The method of conditions extraction discussed above reduces the error when measuring caused by different current and SOC. But as a long-term tracking experiment of the actual vehicle, which does not have the battery pack temperature regulation function, the temperature difference is inevitable. The resistance of each cell in packs fits normal distribution too, verified by the Kolmogorov–Smirnov test. The proportion of resistance of each cell accorded with normal distribution in each group is more than 97%, makes the standard deviation of resistance as the coefficient of inconsistency reasonable. In the paper, the inconsistency recession is characterized by standard deviation of the resistance of each battery pack. Fig.3 shows how inconsistency of the internal resistance changes with the cumulative. Y-axis on the right side is the average temperature inside the battery pack. It can be seen that the standard deviation of resistance does not increased significantly with the power accumulating, but temperature has certain relevance with the changes of temperature.
3555
Caiping Zhang et al. / Energy Procedia 105 (2017) 3551 – 3556 35
0.00015
0.00012
0.00005 10
Inconsistency of the internal resistance Temperature inside the battery pack
0.00000 0
25 0.00008
20 15
0.00004
10 5 Inconsistency of the internal resistance Temperature inside the battery pack
0.00000
0 10000 20000 30000 40000 50000 60000 70000
Temperature/ȭ
20
Standard deviation/Ω
0.00010
30
Temperature/ȭ
Standard deviation/Ω
30
0
10000
20000
30000
40000
50000
0 60000
Cumulative capacitance/Ah
Cumulative capacitance/Ah (a)
(b)
Figure 3.Change curve of standard deviation of the resistance and temperature inside the battery pack in different bus (a) Bus A; (b) Bus B
A scatterplot with temperature and the standard deviation of resistance is shown in Fig.4. As the temperature increases, the standard deviation of internal resistance in the battery pack is decreasing. 1.4x10-4
Standard deviation/Ω
1.4x10-4
Standard deviation/Ω
1.2x10-4 1.0x10-4 8.0x10-5 6.0x10-5 4.0x10-5 2.0x10-5 5
10
15
20
25
30
1.2x10-4 1.0x10-4 8.0x10-5 6.0x10-5 4.0x10-5 2.0x10-5 5
35
10
15
20
25
30
35
Temperature/ȭ
Temperature/ȭ (a)
(b)
Figure 4.Scatterplot with temperature and the standard deviation of resistance in different bus (a) Bus A; (b) Bus B
We do the correlation analysis between temperature and standard deviation of the resistance with Pearson correlation analysis. The results are shown in Table 3, which presents significant relationships for both Bus A and Bus B. The temperature and standard deviation of the resistance is highly negative relevant, compared to the cumulative capacitance. The formula of Pearson correlation coefficient is given as follow.
r
¦ X ¦Y ¦ XY N (¦ X ) (¦ Y ) )(¦ Y N N 2
(X 2
2
(2)
2
)
Where X is the collection of points x, Y is the collection of points y, N is the total number of points. Table 3.correlation analysis between temperature and standard deviation of the resistance Number of valid statistics
correlation coefficients
significance˄P˅
analysis results
Bus A
117
-0.873
0
high negativity relevant
Bus B
98
-0.902
0
high negativity relevant
3556
Caiping Zhang et al. / Energy Procedia 105 (2017) 3551 – 3556
4. Conclusion The operational data of battery packs used in two electrified trolley buses are collected and analyzed. The cell to cell variations of a battery pack are divided into dynamic and static inconsistency, which result from different affecting factors. At the static aspect, inconsistency factors of open circuit voltage in battery packs are the initial SOC inconsistency and accumulated capacity. The relationship of the standard deviation of OCV change models, which is between initial state and changes after some period of usage, is expressed by the regression model. The quantic polynomial system is proved with the highest accuracy on the basis of error analysis. At the dynamic aspect, main inconsistency factor of resistance is the battery temperature compared to battery degradation based on the results of correlative analysis. Three-dimensional model of temperature and initial state with inconsistency of OCV will be further investigated, and the analysis of the SOC and endurance mileage affected by different inconsistency factors will be pursued in our future studies. Copyright Authors keep full copyright over papers published in Energy Procedia Acknowledgements The authors are grateful for financial support via major national research and development projects (Grant No. 2016YFB0101800). References [1] WANG J, SUN Z, WEI X, et al. Research on power battery cell classification method for electric vehicles. J J Chinese Journal of Power Sources; 2012, 1: 036. [2] LI X, PAN H. Study on the uniformity of storage batteries. J Chinese Battery Industry; 2005, 5: 007. [3] Wang Z, Sun F, Zhang C. Study on inconsistency of electric vehicle battery pack. J Chinese Journal of Power Sources; 2003, 27(5; ISSU 158): 438-441. [4] ZHANG B, LIN C, CHEN Q. Analysis and modeling of nonuniformity characteristics of tractive Li-ion batteries. J J Chinese Battery Industry; 2008, 2: 011. [5] WANG J, SUN Z, WEI X, et al. Research on power battery cell classification method for electric vehicles. J J Chinese Journal of Power Sources; 2012, 1: 036. [6] Yang Fan. Inconformity of li battery pack and remedial measures. J Auto Electric Parts; 2014 (5): 37-40. [7] Hai-feng D A I, Nan W, Xue-zhe W. A research review on the cell inconsistency of Li-ion traction batteries in electric vehicels. J Automotive Engineering; 2014, 2: 181-188. [8] Lin C, Wang Y, Chen Y, et al. Test and modeling of nonuniformity characteristics of a Ni-MH battery pack for electrical vehicle. J Chinese Journal of Power Sources, 2005, 29(11): 750. [9] Li X, Jiang J, Zhang C, et al. Robustness of SOC Estimation Algorithms for EV Lithium-Ion Batteries against Modeling Errors and Measurement Noise. J Mathematical Problems in Engineering; 2015, 2015. [10] Teng L, Lin C T, Chen Q S. Inconsistency analysis of LiFePO4 battery packing. J Trans. Tsinghua Univ.(Sci; 2012: 1001-1002. [11] WANG Z, Sun F C. Study on the attended mode of the EV battery pack. J Battery Bimonthly; 2004, 34(4): 279-281. [12] CHEN P, LI Y, ZHANG J, et al. Impact of discharge current strength on battery group consistency. J Chinese Journal of Power Sources; 2013, 3: 031. Caiping Zhang She is an associate professor of Beijing Jiaotong University. Her main research direction is with battery modeling, states estimation, battery charging optimization, battery second use technology and battery energy storage system. E-mail:[email protected].
ScienceDirect Energy Procedia 105 (2017) 3551 – 3556
The 8th International Conference on Applied Energy – ICAE2016
Study on battery pack consistency evolutions during electric vehicle operation with statistical method Caiping Zhanga,b,*, Gong Chenga,b, Qun Juc,Weige Zhanga,b, Jiuchun Jianga,b, Linjing Zhanga,b a
National Active Distribution Network Technology Research Center (NANTEC), Beijing Jiaotong University, Beijing, 100044, China b Collaborative Innovation Center of Electric Vehicles in Beijing, Beijing Jiaotong University, Beijing 100044, China c Lithium Battery Product Quality Supervision and Inspection Center, Zaozhuang, Shandong Province,China
Abstract: The consistency among lithium-ion battery pack is an important factor affecting their performance. In order to investigate the battery pack consistency evolutions and influencing factors from statistics point of view, long-term battery data of two trolley buses are collected. Two parameters including the internal resistance and open-circuit voltage (OCV) are chosen to describe battery pack consistency in the study. The mathematical relationship between the battery pack OCV standard deviation after a period time and the intimal standard deviation with polynomial model is established. It is proved that the model error is within 6%. It is demonstrated that battery temperature has the greatest impact on the internal resistance consistency of the battery pack through correlation analysis. The initial SOC inconsistency and temperature of the battery are two key factors affecting the battery pack consistency based on the operation data, providing a foundation for battery consistency improvement.
© Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license © 2017 2016 The The Authors. Authors. Published Published by by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or under responsibility of ICAE of the 8th International Conference on Applied Energy. Peer-review underpeer-review responsibility of the scientific committee Keywords: Lithium-ion battery pack, consistency, modeling, correlation analysis
1. Introduction With the rapid development of electric vehicles, lithium-ion batteries are increasingly being used in automotive energy source. Since the batteries with good manufacturing start to show consistency after being used for a period of time, further research has been done on consistency caused by increasing usage time of electric vehicles on an international scale. In the long-term charge-discharge process, the differences among the individual cells of the charge and discharge capacity, self-discharge rate, degradation rates in the battery pack will lead to increasingly large gap between the available capacities of each cells [1-4], battery packs makes inconsistencies become an important factor affecting battery performance [5]. The consistency of OCV is one of the most intuitionistic performances of battery packs inconsistency. The standard deviations and range is mostly provided as a parameter representing the dynamic characteristic. Another intuitionistic performance is the resistance or impedance, which is analyzed through electrochemical impedance spectroscopy (EIS). Current research on battery consistency is mostly based on the laboratory experimental data. However, in the actual vehicle running condition data accuracy, sampling frequency and the experimental conditions is limited, which is not fully consistent with. Through long-term tracking of the data, we discussed the statistical laws and influencing factors of two kinds of inconsistency in battery pack, including the open circuit voltage inconsistency and the resistance consistency, which describe the consistency from aspects of battery thermodynamics and kinetic dynamics, *Corresponding author. Tel.: +86-10-51683907; fax: +86-10-51683907. E-mail address: [email protected].
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy. doi:10.1016/j.egypro.2017.03.816
3552
Caiping Zhang et al. / Energy Procedia 105 (2017) 3551 – 3556
respectively. Effectively classifying and quantifying inconsistency is helpful for analyzing the causes, effects and changes in characteristics. The remainder of this paper is organized as follows. Section II describes two definition of the inconsistency selected for study in this paper, which is inconsistency of OCV and resistance. The distribution and variation statistics are discussed in section III. A new model structure is introduced that a quantic polynomial system is acceptable for the standard deviation of OCV change models. A highly negative relationship is proved between temperature and standard deviation of the resistance, compared to the cumulative capacitance. Finally, Section IV concludes with a summary of the main findings of this paper and a highlight of related open issues [6-9]. 2. Evaluation parameters of the battery pack inconsistency The inconsistency of battery pack means inconsistent performance indicators exhibited in the group consisting of batteries. These performances include the available capacity, the Ohmic resistance and polarization resistance, polarization capacitance, temperature characteristics and the recession velocity, etc. These differences in operation will be unified shows in different output parameters [6]. Taking into account the high error rate and lower accuracy of the actual vehicle data, in the study, the open-circuit voltage and the internal resistance of the battery pack are chosen as the evaluation parameters of inconsistency. 2.1 The definition of the inconsistency of the OCV After standing for a whole night, the polarization voltage of battery pack in electric vehicles is fading. The battery management system (BMS) will record the open-circuit voltage of each cell before EV bus start at the next day. The OCV standard deviation of the battery pack, as the inconsistency coefficient on homeostasis parameter characteristics, excludes the impact of current and temperature field caused by the difference. It is an important factor of inconsistency of the pack, but also belong to reversible inconsistent, which can be used as an important reference for improved battery balancing strategy [7-9]. 2.2 The definition of the inconsistency of resistance Due to the different production process, decay rates and temperatures of the cells in the pack, the resistance exhibit differences. When the current through, it will cause greater standard deviation of voltage and greater difference in temperature field. Thereby further increase the inconsistency of the battery pack. The definition of resistance in this article is the resistance derived from the first-order RC model. Identify each piece of the battery parameters, the standard deviation of internal resistance of the battery pack can be calculated. Since disassembly the battery pack is difficult, resistance is defined as the irreversible part of the inconsistency [3,10-12]. In this paper the experimental data is the usage data for up to 7 months of battery packs in two electric trolley buses (text named Bus A and Bus B). It’s pure electric vehicles, but there are pantograph as an external power supply in some sections during operation, which can running and charging in the meantime. So the using conditions is closer to hybrid vehicles, high-current charge and discharge are mixed during running. The battery pack is connected with 3 NMC (LiNixMnyCozO2) batteries in parallel and 104 in series, packed into four battery packs (named group 1, Group 2, Group 3 and Group 4). Initial total capacity is 105Ah, capacity of each cells is 35Ah 3. The inconsistent parameter distribution and variation statistics 3.1 Analysis of the statistical regularities of the open circuit voltage 3.1.1 Analysis of the open circuit voltage distribution Single cell voltage in the battery pack is different. Its distribution is more close to normal. To determine the standard deviation as the inconsistency coefficient of open circuit voltage is rational. This paper tests the significant of normal distribution of data with the Kolmogorov–Smirnov test. Under normal circumstances, when the P value is greater than 0.05, the assumption that the data obey a normal distribution is proved. We verify the normal distribution of the open circuit voltage in Group 1 Bus A with the Kolmogorov–Smirnov test. The P value distribution is shown in Figure 1. The left y-axis is the frequency of P value occurrence. The right is the percentage of frequency of P value occurrence cumulative from small to large. There are only two points of P value smaller than 0.05 in the group, which doesn't coincided with normal distribution, accounting for 1.4% of the overall
3553
Caiping Zhang et al. / Energy Procedia 105 (2017) 3551 – 3556
20
Frequency of occurrence
18
Frequency of occurrence Cumulative Percentage
16
100 80
14 12
60
10 8
40
6 4
20
2 0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cumulative Percentageͧ%ͨ
proportion. Considering the actual operation of the BMS data often appear errors and instability, a small percentage of error is acceptable. The statistical results of the Kolmogorov–Smirnov test on daily open-circuit voltage in eight groups of two vehicles battery packs is shown in Table 1. Although the Bus B running at the similar times with Bus A, but the open circuit voltage failed to stabilize the recording of each day before start. So the effective open circuit voltage data is only half of the Bus A. Since the effective point average distribute in the entire time is more than one hundred days, the Statistical inconsistent of data changes with the continued using is still valid.
0
Statistical distribution of P value in Group 1 Bus A
Figure 1.Statistical distribution of P value texted by K-S with daily open circuit voltage Table 1.The proportion of open-circuit voltage accorded with normal distribution in each group Number of valid statistics
Number of abnormal distribution
percentage of abnormal distribution
Group 1 Bus A
138
2
98.6%
Group 2 Bus A
138
0
100%
Group 3 Bus A
138
1
99.3%
Group 4 Bus A
138
0
100%
Group 1 Bus B
61
0
100%
Group 2 Bus B
61
0
100%
Group 3 Bus B
61
0
100%
Group 4 Bus B
61
0
100%
3.1.2 Standard deviation of open circuit voltage variation analysis and modeling Up to the current study two trolley buses have being used for 160 days. We calculate the standard deviation of open circuit voltage of battery packs in two buses each day. Then we extract voltage and current data about three minutes under predetermined conditions, identify the parameters and calculate the standard deviation of internal resistance of the cells in each group. As the result shown in Fig.2 and Fig.3.Since the trolley bus daily usage is not the same, there may be a few days to repair the bus without using. Therefore the abscissa is the cumulative power of battery to indicate the status of the battery usage. The four groups of batteries in the same bus connect in series, which experience the same current conditions. Difference in manufacture, installation, temperature and vibration would cause the inconsistency of battery pack. And the two buses run on the same bus line, so the environmental temperature and the daily usage time in normal operation is substantially the same. It is clearly shown in Figure 2 that the variation tendency of standard deviation of OCV is closely, and the value is different. We evaluate the standard deviation of OCV in 4 battery groups in each Bus. Because two packs of data are not enough for accurate results evaluated by regression analysis. In this paper, the standard deviation of 8 groups of batteries in two buses are used to evaluate mathematical models, and the one of two packs of batteries in each buses are used to compute the model error. By means of the nonlinear regression analysis for a mathematical model, the equation of standard deviation before used and after using at different cumulative capacitance is given as follow.
Caiping Zhang et al. / Energy Procedia 105 (2017) 3551 – 3556
0.008
Standard Deviation/V
Standard Deviation/V
3554
0.007
0.006
0.005
0.004
Bus B
0.003 0
10000
20000
30000
40000
50000
60000
0.008
0.007
0.006
0.005
0.004
0.003 -10000
Cumulative Capacitance/Ah
Bus A 0
10000 20000 30000 40000 50000 60000 70000
Cumulative Capacitance/Ah
(a)
(b)
Figure 2.Standard deviation of open circuit voltage curve in different bus (a) Bus A; (b) Bus B
V 27584Ah -5.28*1011 * V 05 +1.18*1010 *V 04 -1.03*108 *V 03 +4.42*105 *V 02 -921.56*V 0 +0.7562 V 36423Ah -2.84*1011 * V 05 +6.13*109 *V 04 -5.17*107 *V 03 +2.12*105 *V 02 -423.81*V 0 +0.3355 V 46263Ah -9.61*1010 * V 05 +1.99*109 *V 04 -1.60*107 *V 03 +6.12*104 *V 02 -111.50*V 0 +0.0821
(1)
V 57059Ah -1.97*10 * V +4.27*10 *V -3.60*10 *V +1.47*10 *V -288.99*V 0 +0.2260 11
5 0
9
4 0
7
3 0
5
2 0
Where σ0 is the initial standard deviation of OCV, σxAh is the standard deviation when the cumulative capacitance is xAh. We use the data of battery pack for validation of the model. The initial standard deviation of OCV in Bus A is 0.00518V, and 0.00394V in Bus B. The equations of error calculation is (Simulation value-Actual value)/Actual value*100%.The result is shown as follow, which shows that a quantic polynomial system is acceptable for the standard deviation of OCV change models. Table 2. Prediction of standard deviation model error Cumulative capacitance /Ah
Bus A Actual value
Simulation value
Error
Bus B Actual value
Simulation value
Error
27584
0.00683
0.00657
-3.89%
0.00685
0.00657
-4.14%
36423
0.00707
0.00744
5.20%
0.00759
0.00744
-2.01%
46263
0.00698
0.00736
5.46%
0.00723
0.00736
1.87%
57059
0.00712
0.00749
5.25%
0.00747
0.00749
0.21%
3.2 Analysis of the statistical regularities of resistance Resistance is an important parameter to reflect the performance of the battery itself. Its value is reflected not only by the initial state of the batteries and historical recession, but also by the statuses when measuring, like current, SOC and temperature. The method of conditions extraction discussed above reduces the error when measuring caused by different current and SOC. But as a long-term tracking experiment of the actual vehicle, which does not have the battery pack temperature regulation function, the temperature difference is inevitable. The resistance of each cell in packs fits normal distribution too, verified by the Kolmogorov–Smirnov test. The proportion of resistance of each cell accorded with normal distribution in each group is more than 97%, makes the standard deviation of resistance as the coefficient of inconsistency reasonable. In the paper, the inconsistency recession is characterized by standard deviation of the resistance of each battery pack. Fig.3 shows how inconsistency of the internal resistance changes with the cumulative. Y-axis on the right side is the average temperature inside the battery pack. It can be seen that the standard deviation of resistance does not increased significantly with the power accumulating, but temperature has certain relevance with the changes of temperature.
3555
Caiping Zhang et al. / Energy Procedia 105 (2017) 3551 – 3556 35
0.00015
0.00012
0.00005 10
Inconsistency of the internal resistance Temperature inside the battery pack
0.00000 0
25 0.00008
20 15
0.00004
10 5 Inconsistency of the internal resistance Temperature inside the battery pack
0.00000
0 10000 20000 30000 40000 50000 60000 70000
Temperature/ȭ
20
Standard deviation/Ω
0.00010
30
Temperature/ȭ
Standard deviation/Ω
30
0
10000
20000
30000
40000
50000
0 60000
Cumulative capacitance/Ah
Cumulative capacitance/Ah (a)
(b)
Figure 3.Change curve of standard deviation of the resistance and temperature inside the battery pack in different bus (a) Bus A; (b) Bus B
A scatterplot with temperature and the standard deviation of resistance is shown in Fig.4. As the temperature increases, the standard deviation of internal resistance in the battery pack is decreasing. 1.4x10-4
Standard deviation/Ω
1.4x10-4
Standard deviation/Ω
1.2x10-4 1.0x10-4 8.0x10-5 6.0x10-5 4.0x10-5 2.0x10-5 5
10
15
20
25
30
1.2x10-4 1.0x10-4 8.0x10-5 6.0x10-5 4.0x10-5 2.0x10-5 5
35
10
15
20
25
30
35
Temperature/ȭ
Temperature/ȭ (a)
(b)
Figure 4.Scatterplot with temperature and the standard deviation of resistance in different bus (a) Bus A; (b) Bus B
We do the correlation analysis between temperature and standard deviation of the resistance with Pearson correlation analysis. The results are shown in Table 3, which presents significant relationships for both Bus A and Bus B. The temperature and standard deviation of the resistance is highly negative relevant, compared to the cumulative capacitance. The formula of Pearson correlation coefficient is given as follow.
r
¦ X ¦Y ¦ XY N (¦ X ) (¦ Y ) )(¦ Y N N 2
(X 2
2
(2)
2
)
Where X is the collection of points x, Y is the collection of points y, N is the total number of points. Table 3.correlation analysis between temperature and standard deviation of the resistance Number of valid statistics
correlation coefficients
significance˄P˅
analysis results
Bus A
117
-0.873
0
high negativity relevant
Bus B
98
-0.902
0
high negativity relevant
3556
Caiping Zhang et al. / Energy Procedia 105 (2017) 3551 – 3556
4. Conclusion The operational data of battery packs used in two electrified trolley buses are collected and analyzed. The cell to cell variations of a battery pack are divided into dynamic and static inconsistency, which result from different affecting factors. At the static aspect, inconsistency factors of open circuit voltage in battery packs are the initial SOC inconsistency and accumulated capacity. The relationship of the standard deviation of OCV change models, which is between initial state and changes after some period of usage, is expressed by the regression model. The quantic polynomial system is proved with the highest accuracy on the basis of error analysis. At the dynamic aspect, main inconsistency factor of resistance is the battery temperature compared to battery degradation based on the results of correlative analysis. Three-dimensional model of temperature and initial state with inconsistency of OCV will be further investigated, and the analysis of the SOC and endurance mileage affected by different inconsistency factors will be pursued in our future studies. Copyright Authors keep full copyright over papers published in Energy Procedia Acknowledgements The authors are grateful for financial support via major national research and development projects (Grant No. 2016YFB0101800). References [1] WANG J, SUN Z, WEI X, et al. Research on power battery cell classification method for electric vehicles. J J Chinese Journal of Power Sources; 2012, 1: 036. [2] LI X, PAN H. Study on the uniformity of storage batteries. J Chinese Battery Industry; 2005, 5: 007. [3] Wang Z, Sun F, Zhang C. Study on inconsistency of electric vehicle battery pack. J Chinese Journal of Power Sources; 2003, 27(5; ISSU 158): 438-441. [4] ZHANG B, LIN C, CHEN Q. Analysis and modeling of nonuniformity characteristics of tractive Li-ion batteries. J J Chinese Battery Industry; 2008, 2: 011. [5] WANG J, SUN Z, WEI X, et al. Research on power battery cell classification method for electric vehicles. J J Chinese Journal of Power Sources; 2012, 1: 036. [6] Yang Fan. Inconformity of li battery pack and remedial measures. J Auto Electric Parts; 2014 (5): 37-40. [7] Hai-feng D A I, Nan W, Xue-zhe W. A research review on the cell inconsistency of Li-ion traction batteries in electric vehicels. J Automotive Engineering; 2014, 2: 181-188. [8] Lin C, Wang Y, Chen Y, et al. Test and modeling of nonuniformity characteristics of a Ni-MH battery pack for electrical vehicle. J Chinese Journal of Power Sources, 2005, 29(11): 750. [9] Li X, Jiang J, Zhang C, et al. Robustness of SOC Estimation Algorithms for EV Lithium-Ion Batteries against Modeling Errors and Measurement Noise. J Mathematical Problems in Engineering; 2015, 2015. [10] Teng L, Lin C T, Chen Q S. Inconsistency analysis of LiFePO4 battery packing. J Trans. Tsinghua Univ.(Sci; 2012: 1001-1002. [11] WANG Z, Sun F C. Study on the attended mode of the EV battery pack. J Battery Bimonthly; 2004, 34(4): 279-281. [12] CHEN P, LI Y, ZHANG J, et al. Impact of discharge current strength on battery group consistency. J Chinese Journal of Power Sources; 2013, 3: 031. Caiping Zhang She is an associate professor of Beijing Jiaotong University. Her main research direction is with battery modeling, states estimation, battery charging optimization, battery second use technology and battery energy storage system. E-mail:[email protected].