Consistency evaluation and cluster analysis for lithium-ion battery pack in electric vehicles

Journal Pre-proof Consistency evaluation and cluster analysis for lithium-ion battery pack in electric vehicles Jiaqiang Tian, Yujie Wang, Chang Liu, Zonghai Chen PII:

S0360-5442(20)30051-7

DOI:

https://doi.org/10.1016/j.energy.2020.116944

Reference:

EGY 116944

To appear in:

Energy

Received Date: 26 September 2019 Revised Date:

10 December 2019

Accepted Date: 9 January 2020

Please cite this article as: Tian J, Wang Y, Liu C, Chen Z, Consistency evaluation and cluster analysis for lithium-ion battery pack in electric vehicles, Energy (2020), doi: https://doi.org/10.1016/ j.energy.2020.116944. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

Author Contributions Jiaqiang Tian: Conceptualization, Methodology, Software, Validation, Formal Analysis, Investigation, Data Curation, Writing – Original Draft. Yujie Wang and Chang Liu: Conceptualization, Writing – Review & Editing. Zonghai Chen: Idea, Resources, Writing – Review & Editing, Supervision, Project Administration, Funding Acquisition.

Consistency Evaluation and Cluster Analysis for Lithium-Ion Battery Pack in Electric Vehicles Jiaqiang Tian, Yujie Wang, Chang Liu, Zonghai Chen* Department of Automation, University of Science and Technology of China, Hefei, Anhui 230027, PR China Abstract: Consistency is an essential factor affecting the operation of lithium-ion battery packs. Pack consistency evaluation is of considerable significance to the usage of batteries. Many existing methods are limited for they are based on a single feature or can only be implemented offline. This paper develops a comprehensive method to evaluate the pack consistency based on multi-feature weighting. Firstly, the features which reflect the static or dynamic characteristics of batteries are excavated. Secondly, a weighted method of multi-feature inconsistency is proposed to evaluate pack consistency. In which case, the entropy weight method is employed to determine the weight. Thirdly, an improved Greenwald-Khanna algorithm based on genetic algorithm and kernel function is developed to cluster batteries. Finally, nine months of electric vehicle data are collated to validate the proposed algorithms. Meanwhile, the main factor affecting consistency change is analyzed. The results show that with the usage of batteries, the difference between the cells becomes more serious, which weakens the pack consistency. Besides, the relationship between the consistency attenuation rate and the driving mileage can be approximated by a first-order function. The higher mileages will aggravate the pack inconsistency. Moreover, it has been proven that the improved clustering algorithm has stronger robustness and classification performance. Keywords: Battery pack consistency; Multi-feature inconsistency; Entropy weight method; Improved Greenwald-Khanna algorithm. Nomenclature c Number of clusters Cp Polarization capacitance 2 Norm of the square inner product distance Di dj Redundancy of information entropy ej Entropy of jth feature inconsistency Fi Covariance matrix of ith cluster f(Y,V,U) Fitness function J(Y,V,U) Optimization objective function of GK algorithm I Current *

Corresponding author. Z. Chen. E-mail address: [email protected]. 1

λ θi θ*ij ξ η ρi ζ κ τ

Coulomb efficiency Inconsistency of ith feature Normalized inconsistency of jth feature for ith month Inconsistency of the battery pack Consistency of the battery pack Constant for Mi Genetic stop threshold Coefficient of entropy for feature inconsistency Time constant

Jkfgk(Y,V,U) Optimization objective function of KFGK algorithm J’ Gradient of optimization objective function M Fuzzy index Optimization variable of ith cluster Mi N Number of cells pij Proportion of inconsistency for jth feature in ith month Q Battery capacity ri Mean of ith feature Ro Ohmic resistance Rp Polarization resistance s Dimension of sample T Number of genetic evolution ti Time at the point i tij Time from point i to point j Fuzzy partition matrix of data set U Uab Ohmic voltage drop Up Polarization voltage uik Membership of jth feature for ith sample (l) Membership of jth feature for ith sample at uik lth iteration Matrix of the cluster center V vi Centroid of ith cluster (l) Centroid of ith cluster at lth iteration vi xi(j) ith feature for the jth sample Matrix of sample Y yk kth sample δi SDC of ith feature σi SD of ith feature

ωi Γ ∆t σ

Weight of ith feature Convergence precision Sampling time Free parameter for the gauss radial basis function Abbreviations BMS Battery management system CE Classification entropy DWT Discrete wavelet transform ECM Equivalent circuit model EVs Electric vehicles GA Genetic algorithm GAKFGK GA-KF-GK algorithm GK Greenwald-Khanna algorithm KF Kernel function KFGK KF-GK algorithm LIB Lithium-ion battery MDM Mean-different model OCV Open-circuit voltage PC Partition coefficient PCA Principal component analysis RM Rint model RMSE Root mean square error SD Standard deviation SDC Standard deviation coefficient SOB State of balance SOC State of charge SOH State of health SOP State of power TM Thevenin model

1 Introduction With the development of the power system, the fluctuation and demand for electricity are growing significant [1]. The energy storage system provides an effective way to alleviate these issues [2,3]. The lithium-ion batteries (LIBs) with advantages of high energy density, low self-discharge rate, and long service life, are widely used in electric vehicles (EVs) [4,5]. Hundreds of cells are grouped to provide sufficient voltage and power for the load, which also brings consistency problems [6]. There are two factors that affect the consistency of the battery pack. On the one hand, in production, the initial performance is different due to the difference in manufacturing technology and material [7,8]. On the other hand, the inconsonant performance results in an unbalanced current and state of charge (SOC) using range. Besides, due to the 2

upsizing and unitized physical structure, the heat distribution in the battery pack is disequilibrium. The adverse factors directly lead to the inconsistent aging rate between the cells, which further aggravates the pack inconsistency [9,10]. The pack inconsistency may cause the following hazards [11-14]. (a) Loss of capacity. The pack capacity conforms to the barrel effect. The worst cell determines the pack capacity. (b) Loss of life. The pack life is determined by the cell with the shortest life. (c) Increase of ohmic resistance. The cell with a sizeable ohmic resistance will generate more heat during operation, which will accelerate battery aging. 1.1 Literature Reviews According to the literature, the pack consistency refers to two aspects. One is the inconsistency of internal parameters, while another is the inconsistency of external parameters. The differences in the production process, material, and group technology are the main factors that cause internal parameter inconsistency [15]. Ref. [16] shows that the volatilization of lithium in the production process will affect the available capacity and Coulomb efficiency. The ohmic resistance is affected by electrode thickness, contact area and electrolyte [17]. The poor contact between the electrode and the solid electrolyte will form a high ohmic impedance [18]. Due to slight differences in electrode thickness and contact area, the significant inconsistency in ohmic resistance will be caused [19]. The inconsistent ohmic resistance and Coulomb efficiency make the SOC available range of batteries different[20]. Furthermore, the structure of the battery pack is one of the factors that affect the consistency of batteries. In Ref. [21], the characteristics of different pack structures are compared and summarized. The structure with series-connection in parallel is beneficial to the consistency of SOC at the end of discharge, which is suitable for large-scale battery arrays. The structure with parallel-connection in series can provide higher discharge energy, which is suitable for the small-capacity battery pack. The external parameters inconsistency refers to voltage, current, temperature, etc. Although the parallel-connection pack has a better consistency at the initial time, unbalanced currents will generate at the end of discharge [22]. In Ref. [23], a battery pack with 12 series 1 parallel is constructed for equalization test. In the case of unbalance, due to the different performance between cells, the voltage consistency decreases with the increase of discharging depth. Moreover, different battery shapes and heat dissipation structures have diverse effects on the pack heat distribution [24-27]. A reasonable heat dissipation structure can improve the temperature consistency of the battery pack. According to the literature, battery consistency evaluation methods can be divided into three types: signal processing-based, model-based, and information fusion-based. 3

1) Signal processing-based: These methods refer to time-domain analysis and frequency-domain analysis. The impedance spectroscopy can directly reflect the electrochemical characteristics of batteries. In Ref. [28], it is applied to investigate the effect of aging on the pack consistency. Ref. [29] presents a method for evaluating battery voltage consistency based on a discrete wavelet transform (DWT). The voltages are transformed by DWT to identify the battery with similar electrochemical characteristics. Voltage has the advantages of strong real-time performance and easy sampling, which is selected as the feature to evaluate the pack consistency in Refs. [30, 31]. Wang et al. [30] adopt the square of voltage standard deviation coefficient to estimate the state of balance (SOB) for batteries. In Ref. [31], the voltage range coefficient and variation coefficient are employed to evaluate the pack consistency. 2) Model-based: These approaches employ filters or parameter identification algorithms to estimate the battery parameters. Then, the pack consistency is evaluated by the parameter distribution. The equivalent circuit model (ECM) is abstracted from the physical characteristics of batteries. It has the advantages of simplicity, high accuracy and easy calculation [32,33]. Chen et al. [32] apply ECM and the particle filter to estimate pack SOC, and the pack SOC takes as the feature to evaluate the pack consistency. Zhang et al. [33] propose a mean-different model (MDM) to estimate the SOC consistency of the pack. Ouyang et al. [34] propose a method based on mean and difference to evaluate the internal resistance consistency. Jiang et al. [6] analyze the influence of battery capacity, ohmic resistance and SOC consistency on energy utilization. The results show that SOC consistency has the most significant effect on energy utilization. Therefore, SOC is calculated as the feature to describe the pack consistency. 3) Information fusion-based: Compared with the model-based methods, these approaches are model-free. In Ref. [35], a pack consistency evaluation method based on information entropy is proposed. The features refer to the capacity, ohmic resistance, the ratio of charging capacity to charging capacity. Ref. [36] puts forward a multi-parameter evaluation method for the pack consistency based on principal component analysis (PCA). The features include SOC, state of power (SOP), state of health (SOH), temperature, voltage, ohmic resistance. The shortcomings of the previous methods can be summarized as the following aspects. (a) The method based on a single feature is difficult to describe the pack consistency comprehensively. Whose robustness and reliability are poor. (b) The consistency evaluation method with SOC is only applicable to research in the laboratory. In reality, the SOC of EV is estimated by the ampere-hour integral or look-up table. Because of the open-loop method, SOC estimation is easily disturbed by noise, so the robustness of these approaches are poor. 4

(c) Features SOP and SOH estimation rely on the algorithm and model. A large amount of cells in the battery pack makes these approaches need more computing resources, which is unrealistic for the battery management system (BMS). (d) Some methods are only suitable for offline implementation. The impedance spectroscopy method needs to disassemble the battery pack into cells. Then cells are tested separately. (e) Most methods do not analyze the factors that affect the pack consistency, nor quantify the evolution of cells. 1.2 Motivations and Contributions In order to overcome the shortcomings of the existing methods, this paper proposes an online multi-feature weighted method and an improved fuzzy clustering algorithm for battery consistency evaluation. The static and dynamic parameters of the battery are extracted as features, which improves the reliability of the battery consistency evaluation. The improved fuzzy clustering algorithm improves the accuracy of battery classification, and it provides a basis for consistency analysis. In summary, the main contributions of this paper can be summarized as follows: (1) An on-line consistency evaluation approach is proposed for lithium-ion batteries based on multi-feature weighting. (2) The static and dynamic parameters of the batteries are extracted as features. The weights are determined by the entropy weight method, which improves the reliability of consistency evaluation. (3) An improved fuzzy clustering algorithm based on the genetic algorithm (GA) and kernel function (KF) is proposed which improves the accuracy of battery classification. (4) The relationship between the pack consistency and the driving mileage is investigated. The rest of this paper is organized as follows. In Section 2, the data sources are introduced firstly. Then the effects of features ohmic resistance and polarization resistance on the voltage consistency are analyzed. Finally, an improved consistency evaluation method and the clustering algorithm for batteries are elaborated. In Section 3, the battery modeling and feature extraction method are presented. In Section 4, actual EV data are collected to validate the proposed algorithms. Besides, the factors affecting the consistency variation are analyzed. Section 5 summarizes the conclusions. 2 Consistency Assessment Theory In this section, the theoretical methods of feature extraction and consistency evaluation are introduced. 2.1 Data Description The datasets for consistency assessment are collected from a real-world EV bus. Detailed pack 5

parameters are listed in Table 1. The battery pack operates in three states: discharging, charging and resting, as shown in Fig. 1. The cut-off voltages for charging and discharging are 3.65 V and 2.5 V, respectively.

Fig. 1 Voltage curves for different conditions: (a) Voltage curves for driving. (b) Voltage curves for charging. (c) Charging voltage curves without ohmic voltages. (d) Charging voltage curves without polarization voltages. Table 1 Parameters of LiFePO4 battery pack. Parameter

Value

Unit

Total voltage Total capacity Cell nominal voltage Cell capacity

547.2 90 3.2 9

V Ah V Ah

2.2 Consistency Evolution As can be seen from Fig. 1(a), the voltage consistency in period 1 is better than that in period 2. It 6

indicates that the dynamic condition will reduce voltage consistency. It may be due to differences in cell performance. Fig. 1(b) shows the cell voltage curves under constant current charging. It is noted that the battery voltages rise rapidly in the later stage of charging, as shown in period 4. Since cell 8 reaches the cut-off voltage, the charging is ended. However, the lowest voltage in cell 125 with 3.194V. The premature termination of charging makes other cells cannot be fully charged, which seriously affects the pack charging performance. Period 3 shows the voltage responses at the beginning of charging. Because of the difference between ohmic resistance, the voltage deviation is inconsistent. Likewise, some batteries will reach the cut-off voltage prematurely in discharging, which will cause the incomplete utilization of energy. The charging voltage curves removing the ohmic voltage drops are plotted in Fig. 1(c). It can be seen that voltage consistency has been significantly improved, especially in period 5. Fig. 1(d) shows the voltage curves after removing the polarization voltage. The voltage consistency is also enhanced, which is more obvious at the end of charging. In summary, the ohmic resistance and polarization resistance have different effects on voltage consistency. The ohmic resistance and polarization resistance are significant factors affecting the voltage dynamic characteristics [37]. The open-circuit voltage (OCV) is the terminal voltage after standing for a long time. In which case, the internal state of the battery is balanced so that OCV can describe the static characteristics of batteries [38]. In order to evaluate battery consistency comprehensively, both static and dynamic characteristics are considered. In this work, OCV, ohmic resistance, and polarization resistance are extracted as features to evaluate the pack consistency. The standard deviation (SD) can characterize the dispersion degree of a data set. However, SD is not suitable for comparing data with different units or magnitudes. The standard deviation coefficient (SDC) is a dimensionless numerical evaluation index [39]. It is defined as the standard deviation ratio divided by its mean, as shown in Eq. (1).

δi =

σi ri

=

1 N

 xi ( j ) − ri    ∑ ri j =1   N

2

(1)

where δ i denotes SDC of ith feature, which is applied to describe the variation coefficient of the feature. i denotes OCV, ohmic resistance or polarization resistance. σ i and ri denote the standard deviation and mean of ith feature, respectively. xi and N denote ith feature and number of cells, respectively. By definition, SDC is a pure value without units, so it makes sense to compare the dispersion of different data. In

7

this work, we define the square of SDC θi as the inconsistency of ith feature, as Eq. (2).

1 θi = δ = N 2 i

 xi ( j ) − ri    ∑ ri j =1   N

2

(2)

Considering the contributions of OCV, ohmic resistance, and polarization resistance to the pack consistency are different. It is necessary to assign weights to features. Then the battery pack inconsistency ξ can be defined as Eq. (3).

ξ =ωohmθ ohm + ω polθ pol + ωocvθ ocv

(3)

where ωi (i=ohm, pol, ocv) denotes the weight for the feature. The pack consistency η can be defined as:  ω η = 1 − ξ = 1 − ∑  i  i  n  

2  xi ( j ) − ri        × 100% ∑ ri j =1     N

(4)

In the above expression, the weights are crucial parameters. How to determine weight is an essential part of this work. In information theory, entropy is a measure of uncertainty. The higher the amount of information, the smaller the uncertainty, and the smaller the entropy [40]. The entropy can judge not only the randomness of events but also indicate the discreteness of indexes. The higher the discreteness of the index, the more significant the impact on the comprehensive evaluation, the smaller the entropy value. The entropy weight method is an objective weighting method, which determines the weights of indexes according to the observed data [41]. Therefore, compared with the subjective weighting method, the entropy weight method is more reasonable. Before calculating, the data needs to be standardized, as follows:

θij* =

θij − min {θi1 ,θi 2 ,θi 3 } max {θi1 ,θ i 2 ,θi 3 } − min {θi1 ,θ i 2 ,θi 3 }

(5)

where θij and θij* represent the inconsistency of the jth feature in the ith month before and after standardization. Table 2 shows the process of the entropy weight method. Table 2 The implementation process of the entropy weight method [41]. Step 1: Calculate the proportion of inconsistency for jth feature in ith month. pij =

θij*

(6)

n

∑θ i =1

* ij

Step 2: Calculate the entropy of jth feature inconsistency, where κ =In(n) −1 .

8

e j = −κ ∑ pij In ( pij ) n

(7)

i =1

Step 3: Calculate the information entropy redundancy of jth feature inconsistency. d j =1− ej

(8)

Step 4: Calculate the weight of jth feature inconsistency.

ωj =

dj

3

;

3

∑d j =1

∑ ω =1 j =1

j

(9)

j

2.3 Battery Clustering In Section 2.2, a comprehensive evaluation method of the pack consistency is proposed. It describes the consistency from the holistic perspective. In this section, we will evaluate the pack consistency from the single-cell perspective. An improved fuzzy clustering algorithm is developed for battery clustering. The traditional hard clustering method strictly divides the samples into a particular class, and the membership degree is 0 and 1. This partitioning method is too idealized. Most data in real life do not have strict attributes, and its properties may belong to one or more categories [42]. To solve this issue, the Greenwald-Khanna (GK) clustering algorithm of the soft partition method is developed. The traditional GK algorithm needs to initialize cluster centers randomly. If the cluster centers are not appropriately selected, the clustering effect may be weak. Besides, since the sum of the memberships is 1, it is easy to cause the algorithm to be sensitive to isolated points and noise. Therefore, in order to make the algorithm robust to outliers and initial clustering centers. An improved GK algorithm based on GA and KF is proposed, which is named GAKFGK. The GA is used to optimize the clustering center. The KF transforms the samples in the original space into the feature space. The samples in the feature space are divided to get the optimal partition of the original space, so as to improve the clustering performance. In the GK algorithm, the distance from the sample yk ∈ℜ s to the cluster center point νi ∈ℜ s is a square of the euclidean distance Di2 , as Eq. (10) [43].

Di2 = ( yk − vi ) Μ i ( yk − vi ) 1 ≤ i ≤ c,1 ≤ k ≤ N T

(10)

where c denotes the number of categories. s denotes the dimension of the sample. The matrix

M i =  ρi Fi 

−N

Fi −1 is taken as the optimization variable so that each cluster can adjust the distance norm

according to the data local topological structure. ρi is a constant. Fi is the covariance matrix of ith 9

category, which is defined as Eq. (11) [43].

∑ (u ) ( y N

Fi =

m

( l −1)

ik

k =1

− vi(l ) )( yk − vi(l ) )

T

k

∑ (u ) N

( l −1)

(11)

m

ik

k =1

where l denotes lth iteration. The clustering of the data set Y = [ yk ] can be converted to the optimization of the minimum objective function. m ∈ [1, ∞] is a fuzzy index, which determines the degree of ambiguity for all classifications. The objective function is defined as: c

N

J (Y ,V , U )=∑∑ ( uik ) Di2 m

(12)

i =1 k =1

where V =[vi ] , U = [uik ] are the cluster center matrix and the membership matrix, respectively. c

∑u i =1

ik

= 1 1 ≤ k ≤ N,uik ∈ [ 0,1]

(13)

The distance function in the GK algorithm is transformed by KF, which defines the following objective function: c

N

J kfgk (Y ,V , U ) = ∑∑ ( uik )

m

i =1 k =1

( 2 − K (v i , y k ) )

(14)

where K (vi , yk ) is a Gaussian radial basis function, as follows [44]:

K (vi , yk )=e

−

Di2 2s 2

(15)

Let Di2 > 0 , ∀i , k and m > 1 , the gradient J ′( ) is zero for U and V , then the two necessary conditions for the minimum of Eq. (14) can be obtained. −1

uik =

(1 − K (vi , yk ) ) m−1 c

∑ (1 − K (v , y ) ) i

i =1

k

−1 m −1

(16)

N

vi =

∑u k =1 N

K ( v i , y k ) yk

ik

∑u k =1

(17)

ik

K (v i , y k )

In [45], the detailed GA is introduced. The fitness function is applied to evaluate the quality of individuals in the population. In KF-Greenwald-Khanna (KFGK) algorithm, the objective function

J kfgk (Y ,V , U ) of individuals in the population is derived from Eq. (14). According to the definition, when 10

the objective function takes the minimum value, the optimal clustering result is obtained, that is, the classification effect is the best. In other words, the smaller the objective function value, the higher the fitness. Thus, the fitness function is defined by the objective function. The detailed GAKFGK implementation process is shown in Table 3.

f (Y ,V , U ) =

1 = 1+J kfgk (Y ,V , U )

1 c

N

1+∑∑ u i =1 k =1

m ik

(18)

( 2 − K (v i , y k ) )

Table 3 The implementation process of GAKFGK. Step 1: Initialization: set free parameter s of the kernel function, fuzzy index m , convergence precision γ , clustering number c , genetic evolution number T , genetic stop threshold z , etc. Step 2: The clustering centers are randomly generated to form the initial population. Step 3: Calculate the performance indicators of each individual population: J kfgk (Y ,V , U ) ,

f (Y ,V , U ) . Step 4: The t-generation population is selected, crossed and mutated to form the (t+1)-generation population. Step 5: Judge the termination condition. If

f (Y ,V )(t+1) − f (Y ,V )(t ) < z or t>T , go to Step 6, else

t = t + 1 and go to Step 3. Step 6: Decode and output the clustering center matrix. Step 7: Computation of the membership matrix U ( k +1) . Step 8: Computing cluster center matrix V ( k +1) . Step 9: Judge the termination condition. If U ( t+1) − U ( t ) < γ or ∃ i (1 < i < c) , so that

N

∑u k =1

ik

= 0 , go

to the end, else go to Step 7.

3 Battery Modeling The Rint model and the Thevenin model are the conventional equivalent circuit models of lithium-ion batteries [2,46]. The Rint model is comprised of an ideal voltage source and an equivalent resistance. The voltage source represents OCV, and the resistance represents the ohmic resistance. Compared with the Rint model, the Thevenin model adds an RC network, as shown in Fig. 2(a). The RC network is used to describe the polarization effect of the battery. The electrical behavior of the Thevenin model can be expressed by Eqs. 11

(19)-(22).

U p (k ) = e

(

− k ∆t /( R p C p )

U p (k − 1) + 1 − e

− k ∆t /( R p C p )

) R I (k )

(19)

p

SOC (k ) = SOC (k − 1) + ∆t ⋅ I (k ) ⋅ λ / Q

(20)

OCV (k )=k0 + k1 ⋅ SOC (k ) + k2 / SOC (k ) + k3 ⋅ In( SOC (k )) + k4 ⋅ In(1 − SOC (k ))

(21)

U t (k ) = OCV (k ) + Ro I (k )+U p (k )

(22)

where ∆t and I denote the sampling time and current, respectively. Ro , R p and C p denote ohmic resistance, polarization resistance, and polarization capacitance, respectively. λ and Q denote Coulomb efficiency and total capacity, respectively. U t and U p denote terminal voltage and polarization voltage, respectively. ki is the coefficient of OCV-SOC function.

(a)

(b)

Rp

+

+ Cp

OCV

－

-4

200

400 600 Time (s)

800

Error (V)

Thevenin model Rint model

3.3

0.05 0

-0.05

3.2 3.1 0

-2

0.1

Experiment Thevenin model Rint model

3.4

0

-6 0 (d)

3.5

Voltage (V)

Ut I

－ (c)

Current (A)

Ro

2

200

-0.1

400 600 Time (s)

200

400 600 Time (s)

Fig. 2 Comparison of the Rint model and the Thevenin model. (a) The Thevenin model. (b) The profile of the dynamic current. (c) Comparison of verified voltage. (d) Errors of voltage. In order to compare the accuracy of two models, an A123 LiFePO4 battery (2.3Ah/3.3V) is tested by a 12

battery testing system (NEWARE CT-8004-5V200A-NTFA). A thermostat (SUYIDA GDW-100L) provides a constant experimental temperature. Figs. 2(b)-(d) show the comparison results under dynamic conditions of 25 . The error of the Thevenin model is basically within 10mV. But the error of the Rint model is about 25 mV. The (Root Mean Square Error) of Thevenin model and Rint model are 0.0075 V and 0.0217 V, respectively. For the Rint model, significant errors may be due to neglecting the polarization process. In contrast, the Thevenin model has higher accuracy. Therefore, in this work, the Thevenin model is used for theoretical analysis. The methods of battery parameter identification can be divided into two categories: data-driven method and excitation response method [46,47]. Data-driven methods are typically represented by GA and recursive least squares [48,49]. These approaches require a large amount of data to identify parameters. In contrast, the excitation response method is more convenient to implement. The pulse current is injected into the battery, and the parameters are calculated online according to the voltage response. For EVs, batteries need to be charged every day when EVs are not working. Therefore, the model parameters can be identified with the charging data. Fig. 3 shows battery charging voltage curves after standing. Before the point A, the battery is in standing, the internal state is stable. Then a pulse current is applied to the battery at point A. Whereafter, the voltage quickly jumps to point B, then gradually rises to point C, and finally reaches the steady-state at point D. Among them, the voltage difference U ab is the ohmic voltage drop. The voltage difference U bd is caused by the RC network. At point C, the RC network voltage reaches 95% of the steady-state value, i.e.

U bc = 0.95U bd . Based on the above analysis, the following mathematical models are established: U ab (k ) = Ro I (k )

(23)

U bd (k ) = (1 − e− k ∆t / τ ) R p I (k ),tb = 0

(24)

τ=R p C p

(25)

tbc =tc − tb =3τ

(26)

tbd = td − tb

(27)

then, the parameters can be calculated from Eqs. (23)~(27).

13

Ro =

Rp =

(1 − e

U ab (k ) I (k )

U (k )

bd − (3( td -tb )/( tc − tb ))

(28)

) I (k )

(29)

Based on Eqs. (28) and (29), the features Ro and R p can be extracted.

Fig. 3 Voltage responses to the pulse current. (a) The curves of voltage and current. (b) The response curve under the pulse current.

4 Result and Discussion To verify the effectiveness of the proposed methods, nine months of data are analyzed. The mid-monthly data are sifted as the representative for this month. The selected dates are December 18, 2012, January 18, 2013, February 19, 2013, March 16, 2013, April 18, 2013, May 17, 2013, June 16, 2013, July 15, 2013, and August 19, 2013. The time interval is one month, which can ensure the rationality of analysis.

4.1 Consistency Estimation The heating and cooling system ensures that the battery temperature is within the normal range during operation or charging. The charging starts at 1h after the EV ends serving, which ensures that the battery pack is completely cooled. According to the selected data, the SOC of the battery pack is about 50% before charging. Besides, the battery voltage after standing for 1h is extracted as OCV. Fig. 4 plots the statistics of features on December 18, 2012. It can be seen that these characteristics approximately present normal distribution. Ro concentrates around 0.0069 Ω, with a maximum frequency of 102. There are about 14 cells with Ro above 0.008 Ω. Compared with Ro, the distribution of Rp is closer to normal distribution. It mainly distributes around 0.0056 Ω. Similarly, the distribution of OCV is also compact, 14

which mainly concentrates around 3.288 V. Intuitively, the consistency Ro is worse than Rp and OCV. Their standard deviation are 0.00787 Ω, 0.00316 Ω and 0.0361 V, respectively. The standard deviation of Ro is about 2.2 times that of OCV. Therefore, it seems unreasonable to use voltage unilaterally as a criterion for the pack consistency evaluation. In contrast, the consistency evaluation method with multi-feature weighted is more reasonable.

Fig. 4 Feature statistics on 18 December 2012: (a) Ro statistic. (b) Rp statistic. (c) OCV statistic. The results of the pack consistency evaluation are shown in Fig. 5 and Table 4. The upward trend of qi indicates that the consistency of the battery pack is deteriorating. Especially, qocv increase rapidly after March 2013. According to the entropy weight method, the weights of features are distributed in Table 4. θ ocv allocates the largest weight of 0.5921 due to its severe dispersion. The weights of θ ohm and θ pol are 0.2367 and 0.1712, respectively. As shown in Fig. 5(d), the long-term recycling makes the difference between the cells more serious, thus reducing the consistency of battery pack.

15

Fig. 5 Battery consistency evaluation results: (a) The histogram of θohm. (b) The histogram of θpol. (c) The histogram of θocv. (d) The histogram of η. Table 4 The result of consistency assessment of 9 months. Date 2012.12.18 2013.1.18 2013.2.19 2013.3.16 2013.4.18 2013.5.17 2013.6.16 2013.7.15 2013.8.19 Weight

θohm

θpol

0.0080 0.0049 0.0087 0.0093 0.0096 0.0142 0.0156 0.0185 0.0202

0.0003 0.0010 0.0008 0.0012 0.0014 0.0016 0.0016 0.0014 0.0024

0.2367 0.1712

θocv

η/% -7

1.47×10 1.65×10-7 1.60×10-7 1.78×10-7 2.27×10-7 4.05×10-7 5.13×10-7 7.52×10-7 9.26×10-7

99.81 99.87 99.78 99.76 99.75 99.64 99.60 99.54 99.48

0.5921

*

Fig. 5 shows the decreasing trend in pack consistency, it is not difficult to find that the consistency decay rate is different. In particular, the pack consistency is rebounded in January. What causes this phenomenon? The first fattors that come to mind are temperature, mileage, and operating conditions. The battery pack is equipped with a complete heating and cooling systems, even in winter, the battery pack is heated by the heating system to the normal temperature range. Similarly, the cooling system will continue to cool the battery 16

in summer, keeping the battery temperature in the normal range, so that the battery performance will not be affected seriously. Besides, due to the complex road conditions and the uncertainty of the driver's behavior, the operating conditions of the battery pack may be different each time. These uncertainties may have a subtle effect on the pack consistency. It is shown as the fluctuation of consistency variation in Fig. 6. Compared with the uncertain factors, the mileage has a more obvious influence on the pack consistency, which affects the major trends in the pack consistency. In this work, those uncertain factors are ignored, and the relationship between the mileage and the pack consistency is mainly explored. Fig. 6(a) shows the statistics of the total mileage and consistency decay rate. The abscissa represents the month. Jan. represents 31 days from 18 December 2012 to 18 January 2013. From the statistical results, it can be seen that when the driving mileage increases, the consistency degradation will be more serious. Especially, during the period from April 18, 2013 to May 17, 2013, the total mileage is 6096 KM. In which case, the battery consistency decay rate exceeds 0.10%. More striking is that the consistency decay rate in January is positive, which means that the pack consistency has been restored. The statistic shows that from December 18, 2012 to January 18, 2013, the total mileage is only 267 KM. It means that the EV has not served for full-month. Due to the series and parallel connection in the pack, self-repairing occurs between cells, which makes the difference between cells gradually reduce, thus improving the pack consistency. During the period from January 18, 2013 to February 19, 2013, the EV is serviced normally with a total driving mileage of over 4000 KM. The excessive mileage makes the pack consistency drop sharply. Fig. 6(b) shows an approximate relationship between the mileage and the pack consistency variation. The results show that the consistency variation is negatively correlated with the mileage, which can be approximately fitted by a first-order function, as Eq. (30). Where y and x represent the consistency variation and mileage, respectively. Overall, excessive mileage will accelerate the decay rate of the pack consistency.

y = −2.507 ×10 −5 x+0.0333

17

(30)

Fig. 6 The relationship between driving mileage and consistency variation. (a) The statistics. (b) The fitting.

4.2 Battery Clustering Analysis The pack consistency is assessed quantitatively in the previous session, this section will evaluate it from a qualitative perspective. As can be seen from Fig. 4, features OCV and Ro , R p have different dimensions and magnitudes. In order to avoid the magnitude of OCV being too large, which leads to the other two features contributing less to clustering, it is necessary to normalize features. Meanwhile, the standardization solves the problem that European distance is meaningless because of different feature dimensions. The clustering results are plotted in Fig. 7. Table 5 shows the results of the numerical evaluation. The partition coefficient (PC) and classification entropy (CE) are effective indicators for evaluating the clustering effect [50]. PC is used to evaluate the degree of separation between classification clusters. When the number of clusters is the same, the bigger the PC, the better the clustering. CE is used to calculate the ambiguity of classification clusters. When the number of clusters is the same, the smaller the CE value, the better the clustering. They are defined as Eqs. (31) and (32).

PC =

CE = −

1 N

1 N

∑∑ ( u ) c

N

i =1 j =1

c

2

(31)

ij

N

∑∑ u i =1 j =1

ij

log(uij )

(32)

Table 5 Numerical values of validity measures. Data

GAKFGK PC

KFGK

CE

PC

CE

GK PC

CE

2012.12.18 0.653 0.520 0.640 0.523 0.628 0.528 18

2013.1.18 2013.2.19 2013.3.16 2013.4.18 2013.5.17 2013.6.16 2013.7.15 2013.8.19

0.681 0.679 0.677 0.844 0.816 0.804 0.891 0.761

0.487 0.489 0.490 0.320 0.364 0.364 0.233 0.442

0.652 0.639 0.650 0.648 0.814 0.800 0.890 0.758

0.488 0.539 0.499 0.582 0.367 0.375 0.234 0.445

0.500 0.615 0.601 0.644 0.652 0.788 0.731 0.756

0.693 0.570 0.501 0.584 0.560 0.388 0.466 0.448

Fig. 7 Battery clustering results: (a) 2012.12.18. (d) 2013.1.18. (c) 2013.2.19. (d) 2013.3.16. (e) 2013.4.18. (f) 2013.5.17. (g) 2013.6.16. (h) 2013.7.15. (i) 2013.8.19. As can be seen from Fig. 7, the performance distribution of the batteries in the first four months is symmetrical, which is roughly divided into two categories. The second cluster is represented by cell 24#, 40#, 48#, 64#, 78#, 84#, 96#, 102#, 114#, 120#, 132#, 138# and 152#, accounting for 8.56% of the total. Their performance is relatively weak compared with other cells. Overall, the pack consistency is relatively good. After March 2013, batteries are gradually divided into three categories. The second cluster is mainly 19

represented by the former batteries. The third cluster refers to 8#, 32#, 57#, 58#, 59#, 60#, 74#, 98#, 104#, 116#, etc. This category is mostly separated from the previous cluster 1. It means that the aging rate of batteries is inconsistent with the recycling, which leads to different levels of performance division. The more categories, the worse pack consistency. From Table 5, GAKFGK algorithm has the best clustering indexes, followed by KFGK algorithm. The KF effectively improves the sensitivity of the algorithm to outliers, which makes the algorithm more robust. Compared with KFGK algorithm, GAKFGK algorithm further improves the sensitivity of the algorithm to initial values, the clustering performance is improved. Therefore, the proposed GAKFGK algorithm has better clustering performance for batteries.

5 Conclusion In this paper, battery consistency evaluation methods based on multi-feature weighting and clustering analysis are proposed. The impulse excitation method guarantees the possibility of feature extraction online. The square of SDC avoids unreasonable evaluation problems due to the difference in features units and magnitude. The weighting of dynamic and static features ensures the reliability of the evaluation results. The KF algorithm and the GA algorithm are used to optimize the standard GK algorithm, which improves the convergence performance and robustness of the GAKFGK algorithm. The theoretical analysis and actual data verify the feasibility and effectiveness of the proposed methods. The results show that the parameters R0, RP and OCV have different effects on the consistency of the batteries. Since the feature OCV has the largest dispersion, its weight is 0.5921. With the usage of batteries, the pack consistency is deteriorating. The consistency variation and the mileage can be approximated by a first-order function. The scale factor is -2.507×10-5. The higher mileage reduces the pack consistency, as the battery's performance evolves into multiple clusters. Nine months later, the pack consistency is reduced by about 0.331%. These results are of great significance for engineering applications, especially for battery health management and maintenance. Our future work is to explore the overall factors that affect the pack consistency and to investigate how to improve the pack consistency.

Acknowledgement This work is supported by the National Natural Science Foundation of China (Grant No. 91848111).

Reference [1] Xu B, Wang F, Chen D, et al. Hamiltonian modeling of multi-hydro-turbine governing systems with sharing common penstock and dynamic analyses under shock load[J]. Energy Conversion and 20

Management, 2016, 108: 478-487. [2] Li H, Chen D, Zhang X, et al. Dynamic analysis and modelling of a Francis hydro-energy generation system in the load rejection transient[J]. IET Renewable Power Generation, 2016, 10(8): 1140-1148. [3] Xu B, Chen D, Venkateshkumar M, et al. Modeling a pumped storage hydropower integrated to a hybrid power system with solar-wind power and its stability analysis[J]. Applied Energy, 2019, 248: 446-462. [4] Wang Y, Sun Z, Chen Z. Development of energy management system based on a rule-based power distribution strategy for hybrid power sources[J]. Energy, 2019, 175: 1055-1066. [5] Wei Z, Zhao J, Xiong R, et al. Online estimation of power capacity with noise effect attenuation for lithium-ion battery[J]. IEEE Transactions on Industrial Electronics, 2018, 66(7): 5724-5735. [6] Hu X, Feng F, Liu K, et al. State estimation for advanced battery management: Key challenges and future trends[J]. Renewable and Sustainable Energy Reviews, 2019, 114: 109334. [7] Zhou L, Zheng Y, Ouyang M, et al. A study on parameter variation effects on battery packs for electric vehicles[J]. Journal of Power Sources, 2017, 364: 242-252. [8] Miranda D, Almeida A M, Lanceros-Méndez S, et al. Effect of the active material type and battery geometry on the thermal behavior of lithium-ion batteries[J]. Energy, 2019, 185: 1250-1262. [9] Jannesari H, Khalafi V, Mehryan S A M. Experimental and numerical study of employing Potassium poly acrylate hydrogel for thermal management of 500 Wh cylindrical LiFePO4 battery pack[J]. Energy Conversion and Management, 2019, 196: 581-590. [10] Han X, Lu L, Zheng Y, et al. A review on the key issues of the lithium ion battery degradation among the whole life cycle[J]. eTransportation, 2019, 1: 100005. [11] Zheng Y, Ouyang M, Lu L, et al. Understanding aging mechanisms in lithium-ion battery packs: From cell capacity loss to pack capacity evolution[J]. Journal of Power Sources, 2015, 278: 287-295. [12] Wang L, Cheng Y, Zhao X. A LiFePO4 battery pack capacity estimation approach considering in-parallel cell safety in electric vehicles[J]. Applied energy, 2015, 142: 293-302. [13] Wang Y, Sun Z, Li X, et al. A comparative study of power allocation strategies used in fuel cell and ultracapacitor hybrid systems[J]. Energy, 2019, 189: 116142. [14] Feng X, Ouyang M, Liu X, et al. Thermal runaway mechanism of lithium ion battery for electric vehicles: A review[J]. Energy Storage Materials, 2018, 10: 246-267. [15] Dubarry M, Vuillaume N, Liaw B Y. Origins and accommodation of cell variations in Li‐ion battery pack modeling[J]. International Journal of Energy Research, 2010, 34(2): 216-231. 21

[16] Arunkumar T A, Wu Y, Manthiram A. Factors Influencing the Irreversible Oxygen Loss and Reversible Capacity in Layered Li [Li1/3Mn2/3]O2−Li[M]O2 (M=Mn0.5-yNi0.5-yCo2y and Ni1-yCoy) Solid Solutions[J]. Chemistry of materials, 2007, 19(12): 3067-3073. [17] Tran H Y, Greco G, Täubert C, et al. Influence of electrode preparation on the electrochemical performance of LiNi0.8Co0.15Al0.05O2 composite electrodes for lithium-ion batteries[J]. Journal of Power Sources, 2012, 210: 276-285. [18] Liu T, Ren Y, Shen Y, et al. Achieving high capacity in bulk-type solid-state lithium ion battery based on Li6.75La3Zr1.75Ta0.25O12 electrolyte: Interfacial resistance[J]. Journal of Power Sources, 2016, 324: 349-357. [19] Kisu K, Aoyagi S, Nagatomo H, et al. Internal resistance mapping preparation to optimize electrode thickness and density using symmetric cell for high-performance lithium-ion batteries and capacitors[J]. Journal of Power Sources, 2018, 396: 207-212. [20] Zhang C, Jiang J, Gao Y, et al. Charging optimization in lithium-ion batteries based on temperature rise and charge time[J]. Applied energy, 2017, 194: 569-577. [21] Feng F, Hu X, Hu L, et al. Propagation mechanisms and diagnosis of parameter inconsistency within Li-Ion battery packs[J]. Renewable and Sustainable Energy Reviews, 2019, 112: 102-113. [22] Wu M, Lin C, Wang Y, et al. Numerical simulation for the discharge behaviors of batteries in series and/or parallel-connected battery pack[J]. Electrochimica acta, 2006, 52(3): 1349-1357. [23] Wang Y, Zhang C, Chen Z, et al. A novel active equalization method for lithium-ion batteries in electric vehicles[J]. Applied Energy, 2015, 145: 36-42. [24] Yu K, Yang X, Cheng Y, et al. Thermal analysis and two-directional the thermal management for lithium-ion battery pack[J]. Journal of Power Sources, 2014, 270: 193-200. [25] Zhao J, Rao Z, Li Y. Thermal performance of mini-channel liquid cooled cylinder based battery thermal management for cylindrical lithium-ion power battery[J]. Energy conversion and management, 2015, 103: 157-165. [26] Panchal S, Dincer I, Agelin-Chaab M, et al. Experimental and theoretical investigation of temperature distributions in a prismatic lithium-ion battery[J]. International Journal of Thermal Sciences, 2016, 99: 204-212. [27] Yang N, Zhang X, Shang B, et al. Unbalanced discharging and aging due to temperature differences among the cells in a lithium-ion battery pack with parallel combination[J]. Journal of Power Sources, 22

2016, 306: 733-741. [28] Schuster S, Brand M, Berg P, et al. Lithium-ion cell-to-cell variation during battery electric vehicle operation[J]. Journal of Power Sources, 2015, 297: 242-251. [29] Kim J. Discrete wavelet transform-based feature extraction of experimental voltage signal for Li-ion cell consistency[J]. IEEE Transactions on Vehicular Technology, 2015, 65(3): 1150-1161. [30] Wang S, Shi J, Fernandez C, et al. An improved packing equivalent circuit modeling method with the cell-to-cell consistency state evaluation of the internal connected lithium-ion batteries[J]. Energy Science & Engineering, 2019, 7(2): 546-556. [31] Mechanical Industry Standard of the People's Republic of China, General Requirements for Lithium-Ion Battery Assembly, JB/T 1137-2011. [32] Zhang X, Wang Y, Wu J, et al. A novel method for lithium-ion battery state of energy and state of power estimation based on multi-time-scale filter[J]. Applied energy, 2018, 216: 442-451. [33] Zheng Y, Ouyang M, Lu L, et al. Cell state-of-charge inconsistency estimation for LiFePO4 battery pack in hybrid electric vehicles using mean-difference model[J]. Applied energy, 2013, 111: 571-580. [34] Ouyang M, Zhang M, Feng X, et al. Internal short circuit detection for battery pack using equivalent parameter and consistency method[J]. Journal of Power Sources, 2015, 294: 272-283. [35] Duan B, Li Z, Gu P, et al. Evaluation of battery inconsistency based on information entropy[J]. Journal of Energy Storage, 2018, 16: 160-166. [36] Wang L, Wang L, Liao C, et al. Research on Multi-Parameter Evaluation of Electric Vehicle Power Battery Consistency Based on Principal Component Analysis[J]. Journal of Shanghai Jiaotong University (Science), 2018, 23(5): 711-720. [37] Jiang J, Zhang C. Fundamentals and applications of lithium-ion batteries in electric drive vehicles[M]. John Wiley & Sons, 2015. [38] Wang Y, Liu C, Pan R, et al. Modeling and state-of-charge prediction of lithium-ion battery and ultracapacitor hybrids with a co-estimator[J]. Energy, 2017, 121: 739-750. [39] Wang Z, Chen W, Wang D, et al. A novel combustion evaluation method based on in-cylinder pressure traces for diesel/natural gas dual fuel engines[J]. Energy, 2016, 115: 1130-1137. [40] Xu J, Dang C. A novel fractional moments-based maximum entropy weight method for high-dimensional reliability analysis[J]. Applied Mathematical Modelling, 2019, 75: 749-768. [41] Xiao Q, He R, Ma C, et al. Evaluation of urban taxi-carpooling matching schemes based on entropy 23

weight fuzzy matter-element[J]. Applied Soft Computing, 2019, 81: 105493. [42] Long H, Ali M, Khan M, et al. A novel approach for fuzzy clustering based on neutrosophic association matrix[J]. Computers & Industrial Engineering, 2019, 127: 687-697. [43] Babuka R, Van der Veen P J, Kaymak U. Improved covariance estimation for Gustafson-Kessel clustering[C]//2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No. 02CH37291). IEEE, 2002, 2: 1081-1085. [44] Khaksarfard M, Ordokhani Y, Babolian E. An approximate method for solution of nonlocal boundary value problems via Gaussian radial basis functions[J]. SeMA Journal, 2019, 76(1): 123-142. [45] Javed M S, Song A, Ma T. Techno-economic assessment of a stand-alone hybrid solar-wind-battery system for a remote island using genetic algorithm[J]. Energy, 2019, 176: 704-717. [46] He H, Zhang X, Xiong R, et al. Online model-based estimation of state-of-charge and open-circuit voltage of lithium-ion batteries in electric vehicles[J]. Energy, 2012, 39(1): 310-318. [47] Li X, Wang Z, Zhang L. Co-estimation of capacity and state-of-charge for lithium-ion batteries in electric vehicles[J]. Energy, 2019, 174: 33-44. [48] Zhang C, Allafi W, Dinh Q, et al. Online estimation of battery equivalent circuit model parameters and state of charge using decoupled least squares technique[J]. Energy, 2018, 142: 678-688. [49] Liu C, Wang Y, Chen Z. Degradation model and cycle life prediction for lithium-ion battery used in hybrid energy storage system[J]. Energy, 2019, 166: 796-806. [50] Singh, Nisha, and Vivek Srivastava. Iris Data Classification Using Modified Fuzzy C Means [J]. Computational Intelligence: Theories, Applications and Future Directions-Volume I. Springer, Singapore, 2019. 345-357.

24








Consistency evaluation based on multi-feature weighted for batteries is proposed. The weights of features are determined by the entropy weight method. Consistency evaluation features can be extracted online. An improved fuzzy clustering algorithm is developed to evaluate pack consistency. The proposed methods are validated by nine months of electric vehicle data.

Declaration of interests ☒ 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. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: