A Study via Grey system Theory inLithium-ion Battery Process Impact on the Uniformity of Electricity and Capacity Interrelationship
Chien-Chung Chen and Wu-Shun Jwo
ABSTRACT
During the year of 2008, the petrol price rose to $ 140 per barrel. The threat of energy depletion, environmental awareness rise, and global financial turmoil all result in the impact of car sale. Hence, the development of green energy starts the future development of alternative energy, which makes the instant rise of lithium polymer rechargeable battery in the green supply chain. Currently, countries worldwide are making effort to develop alternative energy sources. Regardless of 3C products or electric vehicles, they require higher quality batteries. Especially, electric vehicle is the main force this century. Although there is no difference on the appearance of electric vehicle and ordinary vehicle, there is difference in the internal composition structure. In order to reduce the burning category components, the motor and controller battery system related components are increased. In this case, the battery is the most critical issue. According to statistics, the sales of electric vehicles will reach 7.29 million until 2018. Among them, up to 85.9% of the electric vehicles select lithium battery as a power source, Therefore, the paper first constructs the lithium-ion battery process impact factor in the uniformity of electricity and capacity interrelationship, and through the grey relational grade and GM(0.N) in grey system theory to analyze the hierarchical relationship of each influence factors. After the practical analysis and calculation, it not only can identify the weighting of each influence factor, but also can be the citing of the making process.
Keywords:Green energy, Lithium battery, Electric vehicle, grey relational grade and, GM(0.N), Weighting
1. Introduction
Since the industrial revolution, human being’s technology and civilization have developed rapidly. This makes a large amount of energy development and utilization. Among them, crude oil is the largest in the energy. International crude oil prices continue to rise since 2004. Moreover, there are turbulences constantly around Persian Gulf oil-producing region in recent years, which makes it worse for the situation of international high crude oil prices. On July, 11th, 2008, New York’s crude oil prices rush to 147.27 US dollar for a barrel. Until the end of 2012, global oil prices are still been maintained at 100 US dollar for a barrel. Under the threat of energy depletion, rising environmental awareness and global financial turmoil, the sales of cars have been impacted. On the other hand, air pollution generated by fossil fuels can’t bear the blame devoted to environmental awareness today. After the world's major industrial countries signed “Kyoto Protocol,” governments are strictly on the amount of carbon dioxide emissions pollution standard. According to Taiwan Environmental Protection Agency statistics, 87.8% of the total amount of domestic air pollution emissions is from mobile sources. It is found that the vehicle emissions arethe prime culprit of air pollution [1~3].
Hence, under the double pressure of energy use efficiency and reduce emissions pollution quantity, each of the major industrial countries and the automobile locomotive industry seeks solutions actively. It is expected to seek a clean and efficient alternative energy, and the battery is considered the first choice. Regardless of 3C products and future electric vehicles, they all require a higher quality battery. Especially in the automotive industry, electric automobile cars (motorcycles) are as the main forces of the century. Although their appearances are not different as ordinary ones, the internal composition structures are different. In order to reduce the combustion components, motor, controller and battery system associated components are added. One of the most critical components is the battery. For car electrical energy, the advantages of electric automobile cars (motorcycles) are that they don’t need to use petrol and the pollution is near zero. Hence, they are much in line with the current energy development and environmental considerations of moving vehicles. However, in the development of electric automobile cars (motorcycles), there are still many adverse factors, including low endurance life, worse high-speed horsepower, bulky and heavy battery, the uneven series battery charging problem, battery life limits, long charging time, the lack of charging spaces and high price. These negative factors are involved to the development of battery technology directly or indirectly, which make it difficult to compete with well-developed internal combustion engine vehicles. According to the statistics, the sales of electric automobile cars worldwide will reach 729 million. Among them, up to 85.9% of the electric cars choose lithium batteries as a power source. It can be predicted that lithium batteries’growth magnitude in the future.Hence, during the cell making-process of battery lithium-ion, it affects the importance of electrically uniformity capacity relationship indirectly, and it is also related to the future development of electric automobile cars (motorcycles).
Due to lithium-ion secondary battery has the advantages of high operating voltage, high energy density, long cycle life, no memory effect, less environmental pollution, rapid charge and discharge and low self-discharge rate; therefore, lithium batteries are expected to gradually expand its market share in the future car battery market. Currently, lithium-ion secondary battery focuses on consumer electronics applications, including laptops, mobile phones, machine tools, digital cameras, multimedia players and game consoles. The electric car market is just 25 billion Yen.
However, it can be predicted in the future that pure electric vehicles will use lithium-ion secondary battery as power supply. So, lithium-ion secondary battery plays the critical role of the development of pure electric vehicles. Because such batteries can charge repeatedly, it can lower the pollution of product manufacturing resource consumption and waste. For the secondary battery technology, it can be divided into two main aspects: energy management technology and manufacturing techniques. In terms of energy management technology, it uses good energy management strategy to raise the use of the secondary battery performance and service life. Currently, there are many relevant researches, such as fast charging, series balance charging and discharging, and parallel charging and discharging strategies [4-17].
Especially on the research topic of series battery balanced charging, they are research focus of battery pack energy management in recent years. In terms of manufacturing technology, the electrode material of lithium-ion secondary battery is the key to battery performance. Since there are many types of the positive and negative active material and electrolyte systems, the industries never stopfor the research and development of electrode materials. In addition to the current under-developed fuel cell research and development stage, with advances in materials and technology, new batteries are developed constantly. It aims to meet the market needs of high energy density, high power density, long life, fast charge capability, high energy efficiency, low self-discharge rate, low-cost, and maintenance-free. Hence, during the cell producing process, some process will affect the electrical difference of celldirectly or indirectly. So, there are grading ranges of the voltage and capacity of each cell. It results in less service life and efficacy of series cell than single cell. Besides, when the battery is during charge and discharge or under the fully charged state, the electrical difference in the single cell will cause stop for charging state of the single cell in multi-series within the battery pack. Finally, it will cause larger differences in the inner cell, and the life and endurance will also be influenced. No matter they are 3C products or future electric car battery packs, they require the highest production process on performance, security, and service life [18,19]. Therefore, production factories are facing electrical deviation interval is too large and the consistency problems during the single cell in the battery pack used in manufacturing. How to solve the problem is the research direction in this paper [20,21].
Section 2 in this paper is the introduction of grey relational analysis and weighting analysis of GM(0,N)[22]. Section 3 introduces production process of lithium-ion batteries plant in Taiwan, and a practical example is used to analyze. In section four, the achieved actual values and practical analysis are included. The actual values are used into a math model to calculate the required values. Finally, the conclusion and future implementation are introduced.
2. The Mathematics Model
2.1 Grey Relational Grade
The mathematical foundation of grey relational grade can be described as follows:
1.Factor space
Assumeis one theme andis one relationship. If a characteristic exists with key factors, such as: countable intention factor, expansion of factor and independence factor for the combination of {;}, {;}, then it can be called a Factor space[23].
2.The comparison of sequence
Assume a sequence as
(1)
and meet the following three conditions
(1) Non-dimensional: Factors must be processed to become non-dimensional.
(2) Scaling: The valueof each sequence belongs to the same order (order difference cannot be greater than 2).
(3) Polarization: Factor description of sequence should be in the same direction.
Thus, this sequence is comparable.
3.The four axioms of grey relational measurement
When the space is formed by meeting factor space and comparability, the space is called grey relational space and is demonstrated by {;}, in which {} is the theme and is the measurement tool. {;} havenormality;duality Symmetric;wholeness andclosenessfour axioms.
According to the above descriptions, if a function can be found to meet all of the above four axioms, is considered as a grey relational grade.
2.1.1The analysis steps of grey relational grade
In grey relational space, exist the sequences.
where , and
(2)
In grey relational grade, if we take as the reference sequence, and the others sequences are inspected sequences, then, it called “localization grey relational grade”, if each sequence can be the reference sequence, then, it called “globalization grey relational grade”. In our research, we focus on Nagai’s grey relational grade[23].
1. Localizationgrey relational grade
(3)
in which
where:
i.: Reference sequence, : Inspected sequences
ii.The difference between and norm).
iii.
iv.
2. The grey relational ordinal
After the grey relational grade is calculated, according the value, we can rank the sequence, and this procedure is called grey relational rank. For reference sequences, and inspected sequences are, if then we found that under the reference sequence, the grey relational rank ofis greater than grey relational rank of
3. Globalization grey relational grade
In the definition of globalization grey relational grade, each sequence can be the reference sequence. In this section, we still use Nagai’s grey relational grade as our mathematics model.
, (4)
when the results are found, we can use the eigenvector method to rank the sequence, and then chose the optimal one. The whole steps are illustrated below.
(1)Constructing the relative weighting matrix, which is called “grey relational matrix”.
(5)
(2)Finding the eigen-value for the relative weighting matrix
(3)Using eigenvector method to find the weighting for each target
(4)The maximumcorresponding eigenvector are the weighting value for whole sequences.
2.2 GM(h,N) Model
In grey system theory, the main function of GM(h,N) model is one of the methods to carry out the calculation of measurement among the discrete sequences and to compensate the shortcomings in the traditional methodology. If in sequences, ,is the main factor in the system, and sequences are the influence factors, then, the GM(h, N) model is defined as[23].
(6)
where: i.andare determined coefficients.
ii.: The major sequence
iii: The influencing sequences.
iii.
If in sequences ,is the main factor in the system, andsequences are the influence factor, then we can use GM(1,N) to analyze the system.
2.2.1 GM(1,N) Model
The GM(1,N) model is defined as
(7)
where:
The analytical steps are shown below.
1. Building the original sequences
(8)
where:
2. Building the AGO sequences
According to the AGO formula, we have
(9)
where:
3. Combining the AGO sequences with the major sequence
(10)
where:
4.Substituting all AGO values into Eq. (10)
(11)
andtransform the equation into matrix form. Eq. (11) will becomes
(12)
5. By using the method to find the values of, where
,
Hence, the relationship between the major sequence and the influencing sequences can be found by comparing the value of.
2.2.2 GM(0,N) Model
The GM(0,N) model is the special case of GM(h,N) model, and is shown below.
(13)
The analysis steps are
1. Substituting the AGO value
(14)
2. Dividingin both sides, then, translate into matrix form
(15)
and assume, wherethen Eq. (15) can be rearranged into
(16)
3. Useto solve the values of,where:，
，
the relationship between the major sequence and the influencing sequences also can be found by comparing the value of.
3. Real Example
The paper uses Exa Energy Technology Co, Ltd.,which produces lithium-polymer battery as an example to analyze the production factors which affect cell’s electrical capacity and uniformity during cell production process. It can provide a basis to adjust production factors during cell production process. Moreover, it makes consistency in the electric of produced cell and improves battery life and security[24].
3.1The Formation and Coding of Assessment Data
First, we collect production factors from lithium-ion cell plants in Taiwan. During the lithium-ion battery production process, we can summarize the production factors as follows: Product process technology; Product process technology; R&D engineering; R&D engineering; R&D engineering; Product process technology;Product process technology and R&D engineering, and they are shown in Table 1
Table 1The influence factor
No. / ContentF1 / Mixing uniform; well mixing
F2 / Coating uniform; well coating
F3 / Press density
F4 / Slitting bur
F5 / Electrode water content
F6 / Electrode tension
F7 / Winding allignment
F8 / Electrode weight
F9 / Iimpurities
F10 / Charge and discharge time
F11 / Charge current
F12 / Electrode scallop
F13 / Deformed cell
F14 / Separator tension
Next, eight production and R&D executives in the company are invited to do professional ratings. The information of the subjects is listed in Table 2, and the ratings are listed in Table 3.
Table 2The eight production and R&D executives
Expert / Expert’s seniority / Experiment positionA / 15 years / Product process technology
B / 8 years / Product process technology
C / 8 years / R&D engineering
D / 8 years / R&D engineering
E / 8 years / R&D engineering
F / 8 years / Product process technology
G / 8 years / Product process technology
H / 12 years / R&D engineering
3.2 Analysis Steps
3.2.1 Grey relational grade
1. Build up the sequences
Let the object is the sequence, then
=A=(10,10,7,10,8,5,6,10,9,7,8,3,5,4)
=B=(10,10,10,10,9,7,7,7,8,10,10,9,9,9)
=C=(10,10,9,8,6,5,7,10,6,8,8,6,8,6)
=D=(9,9,10,10,7,6,8,9,9,8,8,9,8,8)
=E=(10,8,8,2,8,6,3,10,8,5,5,2,4,4)
=F=(9,9,8,9,10,9,10,9,10,9,9,8,9,9)
=G=(10,10,8,10,8,4,5,10,9,6,8,3,5,3)
=H=(10,10,7,10,9,4,6,9,9,5,9,4,6,4)
2. Calculate the globalization grey relational grade
Substitute the data into Eq. (4) and Eq. (5) to find the globalization grey relational grade for each object, the results are shown in Table 4.
Table 4The globalization grey relational grade of the eight production and R&D executives
Expert / Globalization grey relational gradeA / 0.0605
B / 0.0494
C / 0.006
D / 0.0324
E / 0.1518
F / 0.0905
G / 0.028
H / 0.0459
3. Use toolbox to verify the results
By using Matlab toolbox to verify the results, and shown in Fig. 1(a)[25].
3.2.2GM(0,N) method
Based on the characteristic of GM(h,N), we use GM(0,N) to find the weighting for each factor in our paper.
1. Build up the sequences
From the analysis factor, the sequences are
=GGRG=(0.2832, 0.4401, 0.0706, 0.3389, 0.4149, 0.4979, 0.3491, 0.2538
= Mixing uniform; well mixing
=(10, 10, 10, 9, 10, 9, 10, 10)
= Coating uniform; well coating
=(10, 10, 10, 9, 8, 9, 10, 10)
= Press density
=(7, 10, 9, 10, 8, 8, 8, 7)
= Slitting bur
=(10, 10, 8, 10, 2, 9, 10, 10)
= Electrode water content
=((8, 9, 6, 7, 8, 10, 8, 9)
= Electrode tension
= (5, 7, 5, 6, 6, 9, 4, 4)
=Winding alignment
= (6, 7, 7, 8, 3, 10, 5, 6)
=Electrode weight
= (10, 7, 10, 9, 10, 9, 10, 9)
= Iimpurities
=(9, 8, 6, 9, 8, 10, 9, 9)
=Charge and discharge time
= (7, 10, 8, 8, 5, 9, 6, 5)
= Charge current
= (8, 10, 8, 8, 5, 9, 8, 9)
= Electrode scallop
= (3, 9, 6, 9, 2, 8, 3, 4)
= Deformed cell
= (5, 9, 8, 8, 4, 9, 5, 6)
= Separator tension
= (4, 9, 6, 8, 4, 9, 3, 4)
2. Calculate the weighting
Substitute the data into Eq. (16) to find the weighting for each object, the results are shown in Table 5.
Table 5 The weighting of each factor
No. / Factor / WeightingF1 / Mixing uniform; well mixing / 0.0605
F2 / Coating uniform; well coating / 0.0494
F3 / Press density / 0.006
F4 / Slitting bur / 0.0324
F5 / Electrode water content / 0.1518
F6 / Electrode tension / 0.0905
F7 / Winding allignment / 0.028
F8 / Electrode weight / 0.0459
F9 / Iimpurities / 0.088
F10 / Charge and discharge time / 0.0071
F11 / Charge current / 0.1007
F12 / Electrode scallop / 0.1158
F13 / Deformed cell / 0.0013
F14 / Separator tension / 0.0011
3. Use toolbox to verify the results
By using Matlab toolbox to verify the results, and shown in Fig. 1(b)[25].
4. Conclusion
Currently, the cell production factories use classification paired method to solve multi-series pack application. However, because of the electricalinconsistency, it results in more and more interval classification pairing groups. Also, it causesthe production quantity is 1.5 times than the order forms. The analysis in this paper not only provides a reference of production process improvement in the production factories, but also understands the relevant factors which cause abnormal of cell. It points out process direction when exception occurs instead of unitary process. Hence, the paper can be summarized as follows:
1. Collecting the production process of lithium-ion cell plants in Taiwan.