୯ҥᆵ᡼εᏢπᏢଣπ཰πำᏢࣴ‫܌ز‬

ᅺγፕЎ

Graduate Institute of Industrial Engineering

College of Engineering
National Taiwan University
Master Thesis

᎖౷ႝԣғ‫ຼڮ‬යϣϐё᎞ࡋϩ‫!݋‬
Reliability Analysis of
Lithium-Sulfur Batteries in Their Life Cycles

‫ڬ‬դࡏ
Bo-Yen Chou

ࡰᏤ௲௤ǺֆЎБ റγ
Advisor: Wen-Fang Wu, Ph.D.

ύ๮҇୯ 104 ԃ 6 Д
June 2015

i
ύЎᄔा

ҁፕЎԑӧࡌҥ΋ঁԵቾόዴ‫܄ۓ‬ǵаё᎞ࡋࣁ୷ᘵ‫ ޑ‬ኧᏢኳٰࠠඔॊኧᅿ

᎖౷ႝԣ‫ޑ‬ଏϯ౜ຝǴЎύǴ२Ӄගр΋‫ڀ‬ԖѤᅿ‫ރ‬ᄊ‫ޑ‬ଭёϻၸำኳࠠǴаඔॊ

ᏱԖόӕཱུ҅ȐӵҡᏀǵߎឦ਼ϯ‫ނ‬Ϸߎឦȑ᎖౷ႝԣႝ৒ໆᒿк‫ܫ‬ႝԛኧΠफ़

‫ޑ‬ᖿ༈Ǵᡣ‫ૈॺך‬аଭёϻંତኳᔕ٠ᕕှ᎖౷ႝԣႝ৒ໆ‫ޑ‬૰ଏᐒ‫ڋ‬аϷк‫ܫ‬

ႝਔ‫ޑ‬ᡂ౦௃‫ݩ‬ǶԶࡕǴҁፕЎ٩Ᏽ၀ኳࠠϩ‫݋‬ႝԣ‫ޑ‬ტ‫ڮ‬ϩթǵё᎞ࡋǵᡂ౦ኧ

Ϸߥ‫ڰ‬௃‫׎‬฻Ǵаໆϯё᎞ࡋᢀᗺǴ‫؃‬ளႝԣӧҺཀਔ໔‫ޑ‬Ѩਏᐒ౗ǶҁፕЎ೸ၸ

ኧॶϩ‫݋‬ว౜Ǵ‫ࡌ܌‬ᄬ‫ޑ‬ଭёϻኳࠠዴёቶ‫ݱ‬ඔॊӚᅿ᎖౷ႝԣ‫ޑ‬ё᎞ࡋǶҁፕЎନ

а΢ϩ‫݋‬ѦǴΨаଭёϻኳࠠ՘᛾дΓࣴ‫ق܌ز‬Ȩߎឦ‫ނ‬፦‫ཱུ҅ܭ‬ᆶ౷ϯ‫ނ‬բҔё

மϯ᎖౷ႝԣტ‫ڮ‬ȩ
ǴЀ‫ځ‬аᙻ୷݈଺ࣁཱུ҅Ǵዴჴૈ୼ԋфज़‫ڋ‬ႝηϣ೽ӭ౷ϯ

‫ޑނ‬ౢғǴ‫ߏۯ‬᎖ᚆη‫ރ៌ࢲܭ‬ᄊਔ໔Ǵ຾Զ‫ߏۯ‬᎖౷ႝԣტ‫ڮ‬Ƕ

ᜢᗖຒǺ᎖౷ႝԣǵ଼ந‫ރ‬ᄊǵଏϯǵූᎩტ‫ڮ‬ǵଭёϻၸำǵё᎞ࡋϩ‫݋‬

ii
ABSTRACT

The purpose of this research is to utilize reliability engineering theory to investigate

the effects of uncertain factors on the degradation of lithium-sulfur batteries. A Markov

process model is constructed to describe the capacity and capacity degradation of the

battery and evaluate the distribution of its remaining life. A four-state model is found to

be able to describe the fading curves of most lithium-sulfur battery systems having

different cathode materials. It gives detailed insights into the fading mechanisms of

lithium sulfur cells. The model is then used for the analysis of life distribution and

reliability of the battery based on test or observed data. A warranty analysis of the battery

is also presented. It is found that the proposed Markov model is able to describe the

reliability of various kinds of lithium-sulfur battery. It is also verified through the model

that metal oxide has a positive effect for lithium-sulfur batteries with regard to their lives.

Keywords: Lithium-Sulfur Battery, State of Health, Degradation, Remaining Life,

Markov Process, Reliability Analysis,

iii
Ҟᒵ

ύЎᄔा .................................................................................................................ii

ABSTRACT .......................................................................................................... iii

Ҟᒵ ........................................................................................................................iv

კҞᒵ ...................................................................................................................vii

߄Ҟᒵ ....................................................................................................................ix

ಃ΋കǵᆣፕ .........................................................................................................1

1.1 ङඳ ..........................................................................................................1

1.2 ࣴ‫ز‬Б‫ ݤ‬..................................................................................................2

1.3 ࣴ‫ز‬Ҟ‫ ޑ‬..................................................................................................3

1.3 ፕЎࢎᄬ ..................................................................................................3

ಃΒകǵ᎖ႝԣ࣬ᜢ౛ፕཷॊᆶЎ᝘ӣ៝ .........................................................5

2.1 ႝԣ஑ԖӜຒှញ ..................................................................................5

2.2 ᎖ႝԣว৖ཷ‫ݩ‬ᆶКၨ ..........................................................................9

2-3 ᎖ႝԣπբচ౛ᆶ੝‫܄‬........................................................................12

2.4 ᎖౷ႝԣ ................................................................................................14

2-5 Ў᝘ӣ៝................................................................................................16

2-6 λ่........................................................................................................18

ಃΟകǵё᎞ࡋᆶଭёϻၸำཷፕ ...................................................................19

3.1 ё᎞ࡋ࣬ᜢ౛ፕ ....................................................................................19

3.2 ё᎞ࡋᙁϟ ............................................................................................20

3.3 ё᎞ࡋኧ౛ཷፕ ....................................................................................21

3.4 ‫س‬಍ё᎞ࡋ ............................................................................................25

3.5 ଭёϻၸำᙁϟ ....................................................................................25

iv
 3.6 ଭёϻኳࠠϐ੝ਸ‫܄‬፦ ........................................................................27

ಃѤകǵଭёϻၸำኳࠠࡌᄬ ...........................................................................28

4.1 ଭёϻኳࠠࡌᄬ ....................................................................................29

4.2 ᙯ౽ંତᆶᔈҔ ....................................................................................30

4.3 ႝ৒ໆѳ֡ϐόዴ‫ ܄ۓ‬........................................................................31

ಃϖക Ӛᜪձ᎖౷ႝԣ੝‫܄‬௖૸ .....................................................................32

5.1 ଭёϻኳࠠୖኧኳᔕ ............................................................................32

5.2 ႝԣႝ৒ໆΠफ़Ԕጕᆶᡂ౦ኧϩ‫ ݋‬....................................................33

5.2.1 ໺಍᎖౷ႝԣ(LS)к‫ܫ‬ႝϐ૰ଏԔጕ......................................33

5.2.2 ҡᏀମࢎ-᎖౷ႝԣ(Co)к‫ܫ‬ႝϐ૰ଏԔጕ.............................35

5.2.3 Β਼ϯ⑲-᎖౷ႝԣ(‹ʹ)к‫ܫ‬ႝϐ૰ଏԔጕ.........................37

5.2.4 ᙻ୷݈-᎖౷ႝԣ(Ni)к‫ܫ‬ႝϐ૰ଏԔጕ……………………..39

ಃϤക Ӛᜪձ᎖౷ႝԣё᎞ࡋϩ‫ ݋‬.................................................................41

6.1 ཷ‫ۺ‬ϟಏᆶё᎞ࡋ‫ۓ‬က ........................................................................41

6.2 ‫ۓ‬ကႝԣ଼ந‫ݩރ‬ե‫ ܭ‬80%ࣁѨਏΠё᎞ࡋϩ‫݋‬.............................43

6.2.1 ᎖౷ႝԣ(LS)ё᎞ࡋϩ‫݋‬...........................................................44

6.2.2 ᎖౷ႝԣ(CO)ё᎞ࡋϩ‫ ݋‬..........................................................45

6.2.3 ᎖౷ႝԣ(Tiଶ )ё᎞ࡋϩ‫݋‬........................................................46

6.2.4 ᎖౷ႝԣ(Ni)ё᎞ࡋϩ‫ ݋‬...........................................................47

6.3 ‫ځ‬Ѭத‫ـ‬Ѩਏ኱ྗё᎞ࡋϩ‫ ݋‬.............................................................48

6.4 Ӛᜪձ᎖౷ႝԣϐѨਏϩ‫ ݋‬................................................................49

6.4.1 ᎖౷ႝԣ(LS)‫ܭ‬όӕ q ਔё᎞ࡋԔጕ.......................................49

6.4.2 ᎖౷ႝԣ(CO)‫ܭ‬όӕ q ਔё᎞ࡋԔጕ ......................................50

6.4.3᎖౷ႝԣሺ‹ଶ ሻ‫ܭ‬όӕ q ਔё᎞ࡋԔጕ....................................50

6.4.4 ᎖౷ႝԣ(Ni)‫ܭ‬όӕ q ਔё᎞ࡋԔጕ .......................................51

v
 ಃΎക ߥ‫ຼڰ‬ය .........................................................................................52

7.1 ႝԣ଼நԿѨਏк‫ܫ‬ႝԛኧ ................................................................52

7.2 ‫ຼۓڰ‬යΠǴႝԣႝ৒ໆߥ‫୔ڰ‬໔ ....................................................53

ಃΖക ଅ᝘ᆶ่ፕ .............................................................................................56

8.1 ҁፕЎЬाଅ᝘ ....................................................................................56

8.2 ่ፕ ........................................................................................................57

ୖԵЎ᝘ ...............................................................................................................58

ߕᒵ .......................................................................................................................62

vi
კҞᒵ

კ 1 ፕЎࢎᄬკ .....................................................................................................4

კ 2 ႝ৒ໆᒿ๱ൻᕉԛኧሀ෧ᜢ߯კ[5] ............................................................7

კ 3 ࢌൻᕉტ‫ڮ‬ᆶ‫ܫ‬ႝుࡋᜢ߯ϐਢ‫[ٯ‬10] ......................................................8

კ 4 ࠠဦ 18650 ༝ࢊࠠ᎖ᚆηႝԣ޻[14] ........................................................ 11

კ 5 ᎖ႝԣᄬ೷ᆶк‫ܫ‬ႝᐒ‫ ڋ‬...........................................................................12

კ 6 ᎖౷ႝԣк‫ܫ‬ႝҢཀკ ...............................................................................15

კ 7 ଭёϻၸำኳࠠҢཀკ ...............................................................................29

კ 8 Ӛᜪձ᎖౷ႝ৒ໆΠफ़ԔጕКၨ ...............................................................33

კ 9 ᎖౷ႝԣ(LS)ႝ৒ໆኳᔕΠफ़ԔጕᆶჴᡍΠफ़Ԕጕ................................34

კ 10 ᎖౷ႝԣ(LS)ᡂ౦ኧᆶ೯‫ܫ‬ႝԛኧᜢ߯..................................................35

კ 11 ᎖౷ႝԣ(CO)ႝ৒ໆኳᔕΠफ़Ԕጕ .........................................................36

კ 12 ᎖౷ႝԣ(CO)ᡂ౦ኧᆶ೯‫ܫ‬ႝԛኧᜢ߯ .................................................36

კ 13 ᎖౷ႝԣ(‹ଶ ሻႝ৒ໆኳᔕΠफ़ԔጕᆶჴᡍΠफ़Ԕጕ ..........................38

კ 14 ᎖౷ႝԣ(‹ଶ ሻᡂ౦ኧᆶ೯‫ܫ‬ႝԛኧᜢ߯ ..............................................38

კ 15 ᎖౷ႝԣ(Ni)ႝ৒ໆኳᔕΠफ़Ԕጕ ..........................................................40

კ 16 ᎖౷ႝԣ(Ni)ᡂ౦ኧᆶ೯‫ܫ‬ႝԛኧᜢ߯ ..................................................40

კ 17 к‫ܫ‬ႝԛኧ n ‫ۓڰ‬Πё᎞ࡋ .....................................................................42

კ 18 ᎖౷ႝԣ(Ni)᎖౷ႝԣ‫س‬಍ё᎞ࡋҢཀკ ..............................................42

კ 19 q=80%ࣁѨਏΠё᎞ࡋԔጕ......................................................................43

კ 20 ᎖౷ႝԣ(LS)11<n<42 Ԕጕኳᔕ ..............................................................44

კ 21 ᎖౷ႝԣ(CO)17<n<251 Ԕጕኳᔕ ...........................................................45

კ 22 ᎖౷ႝԣ(‹ଶ ሻ38<n<181 Ԕጕኳᔕ.........................................................46

კ 23 ᎖౷ႝԣ(Ni)65<n<301 Ԕጕኳᔕ .............................................................47

vii
კ 24 q=70%ࣁѨਏΠё᎞ࡋϩ‫݋‬......................................................................48

კ 25 q=60%ࣁѨਏΠё᎞ࡋϩ‫݋‬......................................................................48

კ 26 ᎖౷ႝԣ(LS)‫ܭ‬όӕ q ਔё᎞ࡋԔጕ......................................................49

კ 27 ᎖౷ႝԣ(CO)‫ܭ‬όӕ q ਔё᎞ࡋԔጕ .....................................................50

კ 28 ᎖౷ႝԣ(‹ଶ ሻ‫ܭ‬όӕ q ਔё᎞ࡋԔጕ ..................................................50

კ 29 ᎖౷ႝԣ(Ni)᎖౷ႝԣ‫ܭ‬όӕ q ਔё᎞ࡋԔጕ ......................................51

კ 30 к‫ܫ‬ႝԛኧ n ‫ۓڰ‬ΠǴႝԣႝ৒ໆᚈ‫ߞ׀‬ᒘ୔໔ .................................53

კ 31 к‫ܫ‬ႝԛኧ n ‫ۓڰ‬ΠǴႝԣႝ৒ໆൂ‫ߞ׀‬ᒘ୔໔ཷ‫ۺ‬კ .....................54

viii
߄Ҟᒵ

߄ 1 Ӛᅿႝԣ‫ૈ܄‬Кၨ[11, 12]..........................................................................10

߄ 2 Ӛᜪձ᎖౷ႝԣୖኧКၨ ...........................................................................32

߄ 3 ᎖౷ႝԣ LS ଭёϻၸำୖኧ ...................................................................34

߄ 4 ᎖౷ႝԣ CO ଭёϻၸำୖኧ...................................................................36

߄ 5 ᎖౷ႝԣ‹ʹଭёϻၸำୖኧ..................................................................38

߄ 6 ᎖౷ႝԣ Ni ଭёϻၸำୖኧ ....................................................................39

߄ 7 ႝԣ଼நԿѨਏк‫ܫ‬ႝԛኧ ......................................................................52

߄ 8 Ӛᜪձႝԣႝ৒ໆᚈ‫ߞ׀‬ᒘ୔໔ ..............................................................53

߄ 9 Ӛᜪձႝԣႝ৒ໆѰ‫ߞ׀‬ᒘ୔໔ ..............................................................54

ix
ಃ΋കǵᆣፕ

ҁക२ӃᇥܴҁፕЎ‫܌‬ట௖૸‫ޑ‬᎖౷ႝԣӧཥૈྍሦୱ‫ڀ‬Ԗ‫ޑ‬ཀကǴԶࡕଞჹࣴ

‫ز‬Б‫଺ݤ‬рᇥܴǴനࡕගрፕЎ‫ࢎޑ‬ᄬᆶࢬำǶ

1.1 ङඳ

ᒿ㰢ӄౚ࿶ᔮ‫ז‬ೲว৖ǵჹૈྍሡ‫ޑ؃‬όᘐቚߏаϷᕉნԦࢉ‫ޑ‬В੻ᝄख़Ǵᕉߥ

᝼ᚒϷૈྍୢᚒ‫ډڙ‬౜Ϟ‫཮ޗ‬ଯࡋᜢ‫ݙ‬ǴШࣚӚ୯‫ࣴޑ‬วൂՏϷӚεًቷ֡ᑈཱུว

৖٠൨‫؃‬ଯਏ౗ǵ࿯ૈǵଳృ‫ೌמྍૈޑ‬Ǵ٠੝ձଞჹ‫ݨ‬ႝషӝ୏ΚًϷપႝ୏ً

፶຾Չ࣬ᜢࣴวǶ࣬ၨ‫ݨܭ‬ႝషӝ୏Κً፶Ǵપႝ୏ًӧՉᎭၸำύֹӄό཮௨‫ܫ‬

ቲ਻Ǵ೏ຎࣁന٫‫ޑ‬ᕉߥૈྍًǶӢԜǴคፕࢂᐒًǵλ࠼ً‫ࢂ܈‬εࠠЃγǴ֡ё

࣮‫ډ‬પႝ୏ϯ‫ޑ‬೛ीǶႝԣࢂቹៜႝ୏ً‫ૈ܄‬നЬा‫ޑ‬Ӣનϐ΋Ǵว৖ႝ୏ً२Ӄ

ाय़ჹ‫ޑ‬ᜢᗖୢᚒ൩ࢂႝԣ‫ޑ‬ᓯႝૈΚǶࣁΑ௢୏ႝ୏ًଭၲǴႝԣҁ‫ي‬Ѹ໪‫ڀ‬Ԗ

ග‫ߏٮ‬ਔ໔ᒡрεႝࢬ‫ૈޑ‬ΚǴ྽ႝԣූᎩႝໆ෧ϿǴႝᓸ൩཮फ़եǴႝ୏ً‫ޑ‬ଭ

ΚΨ཮෧ϿǶӢԜႝԣᓯӸႝໆ‫ޑ‬ӭჲǴቹៜႝ୏ً‫ុޑ‬ૐΚࣗε[1]Ƕ

ว৖‫ڀ‬Ԗଯૈໆஏࡋǵߏൻᕉტ‫ڮ‬ǵଯӼӄ‫܄‬ǵᆘՅᕉߥ‫ک‬եԋҁ‫ޑ‬Βԛႝԣӧ

ཥૈྍሦୱ‫ڀ‬Ԗख़εཀကǴᆶႉለႝԣǵᙻᙿႝԣ฻໺಍Βԛႝԣ࣬КǴ᎖ᚆηႝ

ԣ‫ڀ‬Ԗ‫ܫ‬ႝႝᓸଯǵૈໆஏࡋଯǵൻᕉტ‫ߏڮ‬ǵᆘՅᕉߥ฻ᡉ๱ᓬᗺǴӢԶِೲ՞

ᏵΑߡឫԄႝη೛ഢǵႝ୏π‫ڀ‬ǵλࠠႝ୏ً฻ሦୱ‫ޑ‬ε೽ϩѱ൑ǶҞ߻Ǵ᎖ᚆη

ႝԣ‫ޑ‬ᔈҔሦୱςᘉ৖Կႝ୏ًؓǵඵૈႝᆛǵ3G ೯ߞǵૐ‫ޜ‬ૐϺǵ୯ٛ฻ӭঁሦ

ୱǴԋࣁΑ 21 Шइന‫ڀ‬ᔈҔ߻ඳ‫ޑ‬ᓯૈᏔҹϐ΋Ƕ

ႝԣଏϯԶԿѨਏ཮Ꮴठౢࠔ‫ૈ܄‬૰ଏǵၮբૈΚ഼ѨǵࣗԿΓ‫ي‬Ӽӄ‫ޑ‬Ӓ্Ǵ

ӢԜǴӧႝԣ࣬ᜢࣴ‫ز‬ύǴዴϪᕕှႝԣ৒ໆ૰ଏᖿ༈࣬྽ख़ाǶࣁૈԖਏ‫ޑ‬ϩ‫݋‬

1
٠ຑ՗ႝԣ‫س‬಍ϐё᎞ࡋǴஒё᎞ࡋϐຑ՗ϒаໆϯ൩ᡂளࡐख़ाǶჹ‫ܭ‬ᇙ೷୘Ϸ

ወӧ٬Ҕ‫ޣ‬೿ࢂ࣬྽ख़ा‫ޑ‬᝼ᚒǶҗ٬Ҕ‫ޣ‬ᢀᗺԶ‫ق‬Ǵё᎞ࡋࡰ኱Ѹ໪ࢂ๊ჹ‫ޑ‬ǵ

ёෳ‫ޑۓ‬ǴЪࢂԖҔ‫ޑ‬ኧॶǴӧԜ‫ॺך‬ёаග‫ٮ‬٬Ҕ‫҅ޣ‬ዴё᎞‫ޑ‬ၗૻǴᡣдॺૈ

ྗዴႣෳႝԣ଼ந‫ރ‬ᄊ(State of Health, SOH)ᆶഭᎩტ‫(ڮ‬Remaining Useful Life,

RUL)Ƕբࣁё᎞ࡋຑ՗ϷКၨਔ‫ޑ‬٩Ᏽǹჹ‫ܭ‬ᇙ೷୘аϷࣴวπำΓ঩Զ‫ق‬Ǵ‫س‬಍

ໆϯё᎞ࡋϩ‫݋‬ёаᔅշ‫פ‬рႝԣൻᕉტ‫ڮ‬ଯ‫ޑ‬চӢǴ٠Ъуа‫ׯ‬๓ǴߡૈԖਏӦ

ගଯႝԣ‫ޑ‬ё᎞ࡋǶ

ӧ᎖ȐᚆηȑΒԛႝԣᡏ‫س‬ύǴཱུ҅‫׷‬਑΋‫ڋࢂޔ‬ऊႝԣว৖‫ޑ‬౟ᓍǴ໺಍‫ޑ‬

ၸ෠ߎឦ਼ϯ‫کނ‬ᕗለᡶ฻ཱུ҅‫׷‬਑ӵ LiCoO2, LiNiO2 ‫ ک‬LiFePO4 ฻Ǵҗ‫ܭ‬ᓯ᎖৒

ໆ‫ޑ‬ज़‫ڋ‬ς࿶ᜤаᅈ‫זى‬ೲว৖‫ޑ‬ѱ൑ሡ‫؃‬ǴӢԜǴ൨‫کפ‬໒วཥࠠଯКૈໆǵӼ

ӄǵ༹ሽ‫׷ཱུ҅ޑ‬਑ࢂҞ߻ࣴ‫ޑز‬዗ᗺǶаൂ፦౷ࣁཱུ҅‫ޑ‬᎖ɡ౷ΒԛႝԣջࣁҞ

߻ന‫ڙ‬ᢋҞ‫ޑ‬ඹжБ‫[ݤ‬1,2]Ǵ‫ځ‬ύ౷ཱུ҅‫ڀ‬Ԗଯ‫ޑ‬౛ፕК৒ໆ(1675 mAh/g)‫ૈک‬ໆ

ஏࡋȐ2600 Wh/kgȑ
ǴЪൂ፦౷‫ڀ‬Ԗሽ਱ե༹ǵၗྍᙦ൤ǵᕉნ϶ӳ฻ᓬᗺǴςԋࣁ

Π΋жଯૈஏࡋ᎖Βԛႝԣ‫کزࣴޑ‬໒ว‫ޑ‬ख़ᗺ[3]ǶҞ߻ౢǵᏢǵ཰ӚࣚςԖ೚ӭ

᎖౷ႝԣ‫࣬ޑ‬ᜢࣴ‫ز‬Ǵ૸ፕӵՖ௦Ҕόӕཱུ҅‫ނ‬፦ٰቚу᎖౷ႝԣ‫ޑ‬ტ‫ڮ‬ǴฅԶ೚

ӭࣴ‫ز‬Ҟ߻ϝฅֽज़‫ೌמܭ‬ᆶ‫׷‬਑ϐ໒วǴࣣаჴᡍኧᏵ଺рঁձཱུ҅ᜪࠠϐϩ‫݋‬

ᆶᇥܴǶϿԖаᐒ౗БԄѐ߄ၲႝԣ৒ໆᒿк‫ܫ‬ႝԛኧϐ໔‫ޑ‬όዴ‫܄ۓ‬Ǵ٠Ъ҂Ԗ

಍΋‫ޑ‬ᐒ౗ኳࠠёаӕਔ૸ፕӚᜪ᎖౷ႝԣ‫ޑ‬੝‫܄‬ǵტ‫ڮ‬ᆶё᎞ࡋǶ

1.2 ࣴ‫ز‬Б‫ݤ‬

᎖ᚆηႝԣ࿶к‫ܫ‬ႝൻᕉ٬Ҕࡕႝ৒ໆ૰ଏ΋ӛࢂ΋ঁεୢᚒǴҞ߻ౢᏢ཰Ӛ

ࣚςගр೚ӭඔॊ᎖ᚆηႝԣႝ৒ໆ૰ଏ‫ޑ‬ኳࠠǴฅԶҞ߻໻ԖཱུϿኧኳࠠૈჹό

ӕᜪձ᎖౷ႝԣ຾Չໆϯϩ‫݋‬ϐКၨǴх֖ႝ৒ໆ૰ଏǵႝԣ଼ந‫ރ‬ᄊǵႝԣഭᎩ
2
ტ‫ڮ‬ǵႝԣයఈ٬Ҕԛኧ [4]ǶӢԜǴҁፕЎගр΋ঁଭёϻ [5]ኳࠠȐMarkov processȑ

ҔаඔॊӚᜪձ᎖౷ႝԣႝ৒ໆ૰ଏ௃‫׎‬ǴԜኳࠠቶ‫ޑݱ‬೏ၮҔӧ่ᄬғ‫ނ‬ᏢǴ‫ځ‬

ჴΨёҔٰᓬϯး࿼Ϸႝ୏ً‫ྍૈޑ‬ᆅ౛ǵှ،ૈྍ‫ٮ‬ᔈ‫ޑ‬ᓬϯୢᚒǵඔॊႝԣӧ

း࿼Ϸႝ୏ًύаϷ୺Չૈྍᆅ౛ᓬϯਔၶ‫ޑډ‬૰ଏၸำ฻ǶҁЎஒᙖҗଭёϻኳ

ࠠǴаόӕᜪձ᎖౷ႝԣ่ᄬᆶ‫ܫ‬ႝ‫س‬಍ࣁ୷ᘵǴඔॊႝԣӧ࿶ᐕ‫؂‬΋ԛк‫ܫ‬ႝൻ

ᕉࡕǴӧόӕёૈ‫ރ‬ᄊύᙯ౽‫ޑ‬௃‫׎‬Ǵаϸࢀ‫؂‬ԛк‫ܫ‬ႝൻᕉࡕϐႝ৒ໆǶԜኳࠠ

ஒ٬‫୼ૈॺך‬ϩ‫݋‬᎖౷ႝԣ‫ޑ‬૰ଏԔጕǴ٠௖‫ځز‬চӢ[6,7]Ƕ

1.3 ࣴ‫ز‬Ҟ‫ޑ‬

ҁЎஒаଭёϻኳࠠඔॊ᎖౷ႝԣ૰ଏ௃‫׎‬Ǵӧ಍΋‫ޑ‬ଭёϻኳࠠࢎᄬΠǴК

ၨόӕᜪձ᎖౷ႝԣ٬Ҕ‫ڀ‬όӕϯᏢ‫܄‬፦ཱུ҅‫ނ‬፦Π‫ޑ‬ႝ৒ໆ૰ଏǵႝԣ଼ந‫ރ‬ᄊǵ

ႝԣഭᎩტ‫ڮ‬ǵႝԣයఈ٬Ҕԛኧϐৡ౦‫܄‬ǶԜኳࠠύ‫ୖޑ‬ኧஒೱ่‫ډ‬ς‫ނޑޕ‬౛

ϯᏢ૰ଏၸำǴаϷཱུ҅‫ނ‬፦‫ޑ‬੝‫܄‬ǴЬाҞ‫ࣁޑ‬ග‫ٮ‬΋ঁ‫ڀ‬ഢ᎖౷ႝԣឦ‫܄‬ǵኧ

ॶໆϯ‫ޑ‬ϩ‫݋‬π‫ڀ‬Ǵаᐒ౗БԄѐ߄ၲႝԣ৒ໆᒿк‫ܫ‬ႝԛኧϐ໔‫ޑ‬όዴ‫܄ۓ‬Ǵ٠

ЪҔ಍΋‫ޑ‬ᐒ౗ኳࠠӕਔ૸ፕӚᜪ᎖౷ႝԣ‫ޑ‬੝‫܄‬ǵტ‫ڮ‬ᆶё᎞ࡋǶຑ՗Ӛᅿόӕ

‫׷ཱུ҅ޑ‬਑‫נ‬᏷Ǵ٠ᙖа௢Ꮴрόӕᜪձ᎖౷ႝԣϐტ‫ڮ‬ϩթǵё᎞ࡋаϷߥ‫୔ڰ‬

໔฻Ƕ

1.4 ፕЎࢎᄬ

ҁࣴ‫ز‬ӅϩࣁΖകǴಃ΋കࣁᆣፕǴϟಏҁࣴ‫ޑز‬ङඳǵ୏ᐒǵࣴ‫ز‬Ҟ‫ޑ‬ᆶ

ࣴ‫ࢎز‬ᄬǹಃΒകࣁ᎖ႝԣ࣬ᜢ౛ፕཷॊᆶЎ᝘ӣ៝ǴЬाϟಏ᎖ႝԣ‫ޑ‬ว৖ᆶ

Ӛ໨ᓬ༈Ǵπբ੝‫܄‬ᆶ૰ଏᆬӢǴ૰ଏኳࠠϐЎ᝘ӣ៝ǹಃΟകࣁё᎞ࡋᆶଭё

ϻၸำཷॊǴϟಏҁࣴ‫ز‬ύ‫܌‬٬Ҕ‫ޑډ‬ଭёϻၸำаϷё᎞ࡋπำϐཷ‫ۺ‬ᆶኧᏢ

ኳࠠǹಃѤകଭёϻၸำኳࠠࡌᄬǴᙖҗଭёϻၸำࡌᄬ᎖౷ႝԣ૰ଏኳࠠࡌ

3
ᄬǴ٠аჴᡍኧᏵ௢Ꮴኳࠠύ‫܌‬ሡाϐୖኧǹಃϖകࣁӚᜪձ᎖౷ႝԣ੝‫܄‬௖

૸ǴаଭёϻኳࠠኳᔕӚᜪձ᎖౷ႝԣ૰ଏ੝‫܄‬٠௖૸к‫ܫ‬ႝԛኧᆶᡂ౦ኧ‫ޑ‬ᜢ

߯ǹಃϤകӚᜪձ᎖౷ႝԣё᎞ࡋϩ‫݋‬ǴаҞ߻നத೏٬Ҕ‫ޑ‬ΟᅿѨਏᖏࣚॶ຾

Չ᎖౷ႝԣё᎞ࡋϩ‫݋‬Ǵ‫פ‬рк‫ܫ‬ႝԛኧᆶႝ৒ໆ૰ଏ‫ڄޑ‬ኧᜢ߯ǹಃΎകߥ‫ڰ‬

ຼය૸ፕǴϩձઠӧ੃຤‫ޣ‬ᆶᇙ೷୘‫૸ࡋف‬ፕ᎖౷ႝԣϐߥ‫ຼڰ‬යǶಃΖകࣁ่

ፕᆶࡌ᝼Ǵᕴ่ҁࣴ‫ز‬ϐࣴ‫่݀ز‬ᆶගр࣬ᜢࡌ᝼‫ٮ‬،฼‫ୖޣ‬ԵǴ຾΋‫؁‬ᇥܴࣴ

‫ز‬ज़‫ڋ‬ᆶ҂ٰࣴ‫ز‬БӛǶ

ಃ΋ക
ᆣፕ

ಃΒക
᎖ႝԣ࣬ᜢཷॊᆶЎ᝘ӣ៝

ಃΟക
ё᎞ࡋᆶଭёϻၸำཷॊ

ಃѤക
ଭёϻၸำኳࠠࡌᄬ

ಃϖക
Ӛᜪձ᎖౷ႝԣ੝‫܄‬௖૸

ಃϤക
Ӛᜪձ᎖౷ႝԣё᎞ࡋϩ‫݋‬

ಃΎക
ߥ‫ຼڰ‬ය૸ፕ

ಃΖക
่ፕᆶ҂ٰࣴ‫ز‬Бӛ

კ 1 ፕЎࢎᄬკ
4
ಃΒകǵ᎖ႝԣ࣬ᜢ౛ፕཷॊᆶЎ᝘ӣ៝

२Ӄଞჹ᎖ႝԣ࣬ᜢӜຒ଺ှញаᗉխࡕុπբ΢‫ޑ‬షౄǴௗ๱ଞჹӚᜪձႝԣ

޻‫ޑ‬ᅿᜪаϷ੝‫܄‬຾ՉຑКǴᇥܴࣁՖ᎖ႝԣ཮೏ᇡࣁࢂ҂ٰ 3C ౢࠔаϷႝ୏ၩ‫ڀ‬

ૈໆᓯӸး࿼‫ޑ‬ЬࢬǶௗ๱ǴаϷ࣬ᜢ౛ፕཷॊǴ٠ჹ‫ܭ‬᎖ႝԣϐπբচ౛ᆶк‫ܫ‬ႝ

੝‫܄‬຾΋‫؁‬௖૸Ǵᙶమ೷ԋ᎖ႝԣტ‫ڮ‬૰ଏϐᆬӢǶനࡕଞჹҞ߻஑ৎᏢ‫܌ޣ‬ගр‫ޑ‬

᎖ႝԣ૰ଏኳࠠ຾ՉЎ᝘௖૸Ǵ‫פ‬рኳࠠࡌᄬ΢౜Ԗ‫֚ޑ‬ᜤᆶज़‫ڋ‬Ϸ‫ځ‬ᓬલᗺǴа଺

ࡕុക࿯ଭёϻኳࠠࡌᄬᆶё᎞ࡋࣴ‫ز‬ϐ୷ᘵǶ

2.1 ႝԣ஑ԖӜຒှញ
ႝԣ‫ޑ‬ሦୱύх֖೚ӭ஑ԖӜຒǴ೯த٬Ҕ‫ޣ‬ჹ‫֖ޑ҅੿ځ‬ཀǴεӭ΋‫ޕ‬ъှǴ

ࣁΑ‫׳‬ుΕΑှႝԣ೭༧ፄᚇЪు༫‫ޑ‬ሦୱǴӃவΑှႝԣ࣬ᜢ‫ޑ‬ӜຒǴωૈ୼Ԗ

҅ዴ‫ޑ‬ᢀ‫ុࡕ଺ٰۺ‬πբ‫ޑ‬ϩ‫݋‬ᆶ௖૸ǶӢԜаΠஒவႝԣಔԋǵᔈҔϷႝ਻੝‫܄‬

‫ޑ‬஑ԖӜຒǴ၁ಒ௶ॊǺ

1. ΋ԛႝԣ(Primary battery)Ǻ྽ႝԣႝΚҔᅰਔǴค‫ݤ‬೸ၸкႝ‫ޑ‬БԄӆံкςᙯ

ϯ௞‫ޑ‬ϯᏢૈǶѱ୧‫ޑ‬ᡵ‫܄‬ႝԣǴᒰଳႝԣǴНሌႝԣ฻ǴࣣឦԜᜪǶ

2. Βԛႝԣ(Rechargeable battery)ǺΒԛႝԣϐ‫ܫ‬ႝၸำ΋ኬࢂ࿶ၸϯᏢૈᙯඤԋ

ႝૈǴՠёᙖҗкႝ‫ޑ‬БԄǴஒႝૈख़ཥ‫ݙ‬ΕႝԣǴख़ཥᙯϯԋϯᏢૈǴԶӆԛ٬

ҔǴӵႉለǵᙻᙿǵᙻణǵ᎖ᚆηႝԣ฻Ƕ

3. ૈໆஏࡋ(Energy density)Ǻ߄ҢБ‫ݤ‬Ԗ‫ٿ‬ᅿǴ΋ࣁᡏᑈૈໆஏࡋ(Wh/L)Ǵќ΋ᅿ

ࣁख़ໆૈໆஏࡋ(Wh/Kg)ǴதҔ‫߄ܭ‬ҢӚᅿϯᏢ‫׷‬਑ൂՏᡏᑈ‫ൂ܈‬Տख़ໆ‫ૈ܌‬ග‫ٮ‬

ӭϿૈໆ‫ୖޑ‬ԵǶ

4. ᚐ‫ۓ‬৒ໆ(Nominal Capacity)Ǻᚐ‫ۓ‬৒ໆǴΨᆀࣁ኱ᆀ৒ໆǶ΋૓ႝԣ‫ޑ‬ᆽႝໆǴ

཮аmAh(డӼ୻λਔ)‫܈‬Ah(Ӽ୻λਔ)ٰ߄ҢǴ྽ႝԣкႫႝࡕǴ‫ܫ‬ႝԿᄒЗႝᓸ

(Cut Off Voltage)ਔ‫ܫૈ܌‬рϐႝໆǴջࣁԜႝԣ‫ޑ‬ᚐ‫ۓ‬৒ໆ[8]Ƕ΋ԛႝԣϐᚐ‫ۓ‬৒

5
ໆǴதᆶ٬Ҕ‫ॄޑ‬ၩԖࡐε‫ޑ‬ᜢ߯Ǵ‫܌‬а೯தόуа኱ҢǶ

5. ႝԣႝໆ‫ރ‬ᄊ(State of Charge)ǺࡰႝԣҞ߻ϣ೽‫܌‬ᓯӸႝໆᆶႝԣёҔႝໆϐ

ԭϩКॶǶჹ‫ܭ‬όӕελೕ਱‫ޑ‬ႝԣ(‫ٯ‬ӵ2 Ahǵ10 Ah)Ǵ྽‫ޑޣٿ‬кႝ‫ރ‬ᄊ΋ኬਔǴ

‫ૈ܌‬ញ‫ܫ‬р‫ޑ‬ႝໆࠅό࣬ӕǶჹ‫ܭ‬SOCനදၹௗ‫ۓࠠڂޑڙ‬ကࣁ[8]Ǻ

SOC 1 
³ i ˜ dt (2.1)
C0

‫ځ‬ύǴ i ࣁᕓਔ‫ܫ‬ႝႝࢬǹ t ࣁਔ໔ǹ C0 ࣁႝԣϐᚐ‫ۓ‬৒ໆǶ

6. ႝԣ଼ந‫ރ‬ᄊ(State of Health, SOH)Ǻႝԣ଼ந‫ރ‬ᄊࡰ‫ࢂޑ‬ᆶӄཥႝԣ࣬КၨΠǴ

‫ځ‬੝‫ۓ‬ϐ‫ރૈ܄‬ᄊ‫ޑ‬ໆෳྗ߾[3]Ƕ࣬ၨ‫ܭ‬SOCԖၨࣁܴዴ‫ۓޑ‬ကǴSOHϐ‫ۓ‬ကၨࣁ

ЬᢀǴёаਥᏵόӕ‫ޑ‬ႝԣ‫ૈ܄‬ԶԾՉ‫ۓ‬ကǴ΋૓ёаԵቾൂᐱ‫܈‬ಔӝӚᅿႝԣୖ

ኧӵႝԣ৒ໆǵ‫ࢬޔ‬ϣߔǵҬࢬߔ‫ל‬ǵԾ‫ܫ‬ႝ౗ǵкႝૈΚࣗ‫܈‬ф౗ஏࡋٰ‫ۓ‬ကǶ

аႝԣ৒ໆࣁ‫ٯ‬ǴSOHёа߄ҢࣁǺ
Cn
SOH ˜100% (2.2)
C0

‫ځ‬ύǴCn ࣁӧಃ n ਔ‫څ‬SOCࣁ100%ਔ‫ޑ‬ႝԣ৒ໆǹ C0 ࣁႝԣϐᚐ‫ۓ‬৒ໆǶᒿ๱ႝԣ

‫ޑ‬٬ҔၸำǴ‫ރ܈ૈ܄ځ‬ᄊஒᒿ๱όё଍‫ނޑ‬౛ϷϯᏢᡂϯ೴ᅌൾϯԶ٬ளႝԣค

‫ݤ‬ᝩុ٬ҔǶᖐ‫ٰٯ‬ᇥǴ΋૓฽૶ࠠႝတϐ᎖ႝԣӧதྕ25ɗΠǴ཮೴ԃफ़ե20%

‫ޑ‬ႝ৒ໆ[8]Ƕ೯தऩႝԣ৒ໆե‫ۈ߃ܭ‬৒ໆ‫ޑ‬80%ǴཀջSOHե‫ܭ‬80% Ǵ߾ႝԣᆅ

౛‫س‬಍ (Battery Management System, BMS)Ǵ཮ගᒬ٬Ҕ‫ޣ‬ᔈ၀Ϸਔ‫׳‬ඤႝԣ[9]Ƕ

7. ‫ܫ‬ႝೲ౗/CК౗(C ratio)ǺҔٰ߄Ңႝԣк‫ܫ‬ႝਔ‫ޑ‬ႝࢬελϐК౗ൂՏǴ‫ٯ‬ӵǴ

а1λਔஒႝԣ‫ܫ‬ႝֹ౥Ǵᆀࣁ1C‫ܫ‬ႝǴϸϐǴ৒ໆࣁ2000 mAH‫ޑ‬᎖ႝԣǴ0.5C߾

ж߄а1000mA຾Չкႝ‫ܫ܈‬ႝǶ

8. ᚐ‫ۓ‬ႝᓸ(Nominal Voltage)Ǻࣁႝԣ҅தπբਔ‫ޑ‬ႝᓸǴ‫ځ‬চ౛ࣁႝԣ҅ॄཱུ‫׷‬

਑ǴӢϯᏢϸᔈ‫܌‬೷ԋϐႝՏৡଯեǶόӕ‫׷ཱུॄ҅ޑ‬਑‫܌‬ౢғ‫ޑ‬ႝᓸόӕǴ ᎖ᚆ

ηႝԣ΋૓ऊࣁ3.6VǶ

6
9. ϣߔ(Internal Resistance)Ǻႝԣࣁ೚ӭϯᏢ‫׷‬਑ಔԋǴ೿Ԗ΋‫לߔޑۓ‬Ǵႝԣ‫ޑ‬

ϣߔଯե۳۳ቹៜк‫ܫ‬ႝ‫ޑ‬੝‫܄‬Ƕ

10. ‫ܫ‬ႝᄒЗႝᓸ(Cut off discharge voltage)Ǻࣁႝԣӧ‫ܫ‬ႝਔǴ‫ډ‬ၲ‫ޑ‬ಖᗺႝᓸǴऩ

ե‫ܭ‬ᄒЗႝᓸϝᝩុ‫ܫ‬ႝǴ߾ႝᓸ཮࡭ុΠफ़Ǵ཮೷ԋႝԣཞᚯǶ΋૓᎖ႝԣ೛‫ۓ‬

ӧ2.6Vɴ3.0VǶ

11. ໒ၡႝᓸ(Open Circuit Voltage,OCV)Ǻႝԣӧคॄၩ‫ޑ‬௃‫ݩ‬ΠǴ҅ॄཱུϐ໔‫ޑ‬ႝ

ՏৡǶ

12. ൻᕉტ‫(ڮ‬Cycle Life): Βԛႝԣӧϸᙟк‫ܫ‬ႝ‫ޑ‬٬ҔΠǴႝԣ଼ந‫ރ‬ᄊ཮೴ᅌΠ

फ़Ǵ೯தа၀ႝԣ‫ޑ‬৒ໆբ኱ྗǴ΋૓ёஒႝԣ଼ந‫ރ‬ᄊफ़Կ80%‫܈‬Կ60%ਔ‫ۓ‬ကࣁ

ႝԣ‫ޑ‬ѨਏǴԜਔϐк‫ܫ‬ႝԛኧǴᆀࣁൻᕉტ‫ڮ‬Ƕ΋૓ٰᇥǴႝԣ‫ޑ‬৒ໆᆶൻᕉԛ

ኧ‫ޑ‬ᜢ߯ёҗკ 2‫܌‬ҢǴࣁ΋ߚጕ‫܄‬ᖿ༈Ƕҗკё࣮рǴӧԐයൻᕉၸำύႝԣ‫ޑ‬

৒ໆሀ෧ೲࡋၨ‫ז‬Ǵӵ୔ୱAǴௗΠٰ৒ໆሀ෧ೲࡋᖿ጗Ǵӵ୔ୱBǴ‫ډ‬Α߈ԭԛൻ

ᕉԛኧሀ෧ςᄌᄌѳᛙǴӵ୔ୱCǴԶ‫ډ‬Αനಖ໘ࢤǴӵ୔ୱDǴ৒ໆሀ෧ᖿ༈ஒӆ

ࡋ࡚ᗊΠफ़ǶฅԶ΋૓௃‫ݩ‬ΠǴத‫ۓ‬က྽ႝԣ৒ໆΠफ़‫ډ‬ᚐ‫ۓ‬৒ໆ‫ޑ‬80%Ǵཀջ྽

SOHࣁ80%ਔǴຎࣁႝԣ‫ޑ‬ѨਏǴ೯தԜ໘ࢤวғ‫୔ܭ‬ୱCǴӢԜႝԣቷ୘ၨϿϦѲ

୔ୱDΠ‫࣬ޑ‬ᜢၗ਑Ƕ

კ 2 ႝ৒ໆᒿ๱ൻᕉԛኧሀ෧ᜢ߯კ[5]

13. ૶Ꮻਏᔈ(Memory effect): ႝԣӧؒԖ‫ֹܫ‬ႝ‫ޑ‬௃‫ݩ‬ΠࡼакႝǴ߾ႝԣ৒ໆё

7
ૈค‫ݤ‬ӣ‫ډ‬চԖ‫ޑ‬НྗǴՠऩஒႝԣம‫ڋ‬ుࡋ‫ܫ‬ႝࡕӆкႝǴ৒ໆёૈ൩ૈӣൺǴ

೯தԜᅿ౜ຝதวғ‫ᙿᙻܭ‬ႝԣ΢ǴԶ᎖ႝԣ߾ค૶ᏫਏᔈǶ

14. ‫ۓ‬ႝࢬ(Constant current, CC)Ǻа‫ޑۓڰ‬ႝࢬჹႝԣкႝ‫ܫ܈‬ႝǶ

15. ‫ۓ‬ႝᓸ(Constant current, CV)Ǻа‫ޑۓڰ‬ႝᓸჹႝԣкႝǴкႝႝࢬ཮ᒿ๱ႝᓸ

ॶௗ߈ԶΠफ़Ǵჹ‫ܭ‬᎖ႝԣкႝ೯த٬ҔCC-CVкႝኳԄǴ߻ࢤ௦ҔCCǴԶ྽ႝԣ

ႝᓸ‫ډ‬ၲ4.2VࡕǴӆᙯҔCVкႝǶ

16. ‫ܫ‬ႝుࡋ(Depth of discharge, DOD)Ǻ‫ܫ‬ႝుࡋཀջჹᚐ‫ۓ‬৒ໆ‫ܫޑ‬ႝໆК౗(%)Ǵ

྽ႝԣ‫ډ‬ၲಖЗႝᓸਔǴ൩߄Ң‫ډ‬ၲΑ100%‫ܫޑ‬ႝుࡋǶவ٬Ҕ࿶ᡍᆶෳ၂ᆶύว

౜Ǵߏයుࡋ‫ܫ‬ႝ཮уೲႝԣ৒ໆ‫ޑ‬૰ଏೲ౗Ƕ‫ܫ‬ႝుࡋჹᔈൻᕉტ‫ޑڮ‬ᜢ߯җკ

3 ൻᕉტ‫ڮ‬ᆶ‫ܫ‬ႝుࡋᜢ߯‫܌‬ҢǴё࣮р߈՟‫ܭ‬΋ঁࡰኧሀ෧ᖿ༈Ǵ྽‫ܫ‬ႝుࡋࣁ

10%ਔൻᕉტ‫ڮ‬ଯၲ5000ԛǴԶ྽‫ܫ‬ႝుࡋࣁ90%ൻᕉტ‫ڮ‬аե‫ܭ‬500ԛǴ࣬ৡࣗ႐Ƕ

კ 3 ൻᕉტ‫ڮ‬ᆶ‫ܫ‬ႝుࡋᜢ߯[10]

ၸ‫ܫ‬ႝ(Over discharge)Ǻ྽ႝԣ‫ܫ‬ႝե‫ܭ‬ᄒЗႝᓸॶǴ߾ᝩុ‫ܫ‬ႝ߾ёૈ೷ԋႝԣ

ᅅన‫܈‬ӍϯǴуೲႝԣტ‫ڮ‬ϐ૰ଏǶ

8
2.2 ᎖ႝԣว৖ཷ‫ݩ‬ᆶКၨ
Ծவႝૈ೏Γᜪว౜٠໒‫ۈ‬εໆ٬ҔаٰǴӵՖஒႝΚ଺Ԗਏ౗‫ޑ‬٬ҔǵᓯӸ

ᆶᆅ౛΋‫ࢂޔ‬΋໨࣬྽ख़ा‫ޑ‬ፐᚒǶவ 19 Шइҷ੝วܴႝԣϐࡕǴߡഌុ໒‫ۈ‬ԖӚ

ᅿόӕᅿᜪ‫ޑ‬ႝԣ೏วܴᆶ٬ҔǴҗ‫ܭ‬όӕᅿႝԣϣ೽‫ޑ‬ႝཱུ‫׷‬਑ǵႝှనᆶᄬ೷

೿όᅰ࣬ӕǴӢԜᗨฅ‫୷ځ‬ҁҞ‫ࣁࣣޑ‬ᓯӸႝૈǴՠӚᅿϯᏢϸᔈᆶႝ਻੝‫ࠅ܄‬ε

࣬೵৥ǶҞ߻ς೏ቶ‫ݱ‬٬Ҕ‫ޑ‬Βԛႝԣх֖ႉለႝԣǵᙻᙿႝԣǵᙻణႝԣᆶ᎖ႝ

ԣ฻฻Ǵ‫ځ‬ύႉለႝԣࣁว৖നԐǵғౢനࣁԋዕЪςၲ‫ډ‬ໆౢ໘ࢤǴӢԜᇙ೷ԋ

ҁΨၨեǴՠ‫ૈځ‬ໆஏࡋᆶф౗ஏࡋ೿ୃեǴ࣬ჹ೷ԋᡏᑈᡂεǵख़ໆୃଯ‫ک‬ൻᕉ

ტ‫ڮ‬฻‫߄ૈ܄‬౜ό٫฻લᗺǴӕਔΨӸӧᕉߥ‫ޑ‬ୢᚒǶᙻᙿႝԣ‫ૈځ‬ໆஏࡋᆶൻᕉ

ტ‫֡ڮ‬ၨႉለႝԣଯЪёၲ‫ډ‬εႝࢬ‫ܫ‬ႝᆶऐၸкႝ/ၸ‫ܫ‬ႝǴՠ‫ڀ‬Ԗкႝ૶ᏫਏᔈǴ

Զᙿ‫ߚ܄ࢥޑ‬தமǴ཮ჹᕉნ೷ԋԦࢉǴҞ߻೚ӭ୯ৎ೿ς࿣ҔǶᙻణႝԣҁ‫ي‬ό

֖ჹΓᡏԖ্‫ߎޑ‬ឦӵႉǵᙿ฻Ǵ‫ૈځ‬ໆஏࡋᆶф౗ஏࡋ֡ଯ‫ܭ‬ႉለႝԣЪ‫ܫ‬ႝు

ࡋᆶ٬Ҕტ‫ڮ‬٫Ǵՠҗ‫ൂܭ‬ႝԣ‫ޑ‬ႝᓸୃեǴ࣬ၨϐΠሡाၨӭ‫ޑ‬ႝԣՍೱωёၲ

‫܌ډ‬ሡ‫سޑ‬಍ႝᓸǴЪϝ‫ڀ‬Ԗ૶Ꮻਏᔈ‫ޑ‬લᗺ[11]Ƕҁࣴ‫ز‬໻ଞჹӚᅿаቶ‫ݱ‬೏٬Ҕ

ϐΒԛႝԣ(Rechargeable battery)ϐ‫ૈ܄‬ᆶᓬલᗺ଺КၨǴӵ߄ 1 ‫܌‬ҢǶ

9
 ߄ 1 Ӛᅿႝԣ‫ૈ܄‬Кၨ[11, 12]

ႝԣᅿᜪ ႉለႝԣ ᙻᙿႝԣ ᙻణႝԣ ໺಍᎖ႝԣ ᎖౷ႝԣ

ૈໆஏࡋ
30 60 80 135 400
(Wh/kg)

ႝ৒ໆ
300 150 800 1200 1675
(mAh/g)

ѳ֡πբ
2V 1.2 V 1.2 V 3.7 V 2.3V
ႝᓸ(V)

ᏹբ
-20~60°C -40~60°C -20~60°C -20~60°C -20~60°C
ྕࡋ୔໔

ൻᕉტ‫ڮ‬ 400 500 500 >500 500

ё‫ז‬ೲк

ёుࡋк ё‫ז‬ೲкႝǵ ႝǵଯф౗

ё‫ז‬ೲк ଯ ф ౗ ‫ܫ‬
‫ܫ‬ႝǵ‫ೌמ‬ ଯф౗‫ܫ‬ႝǵ ‫ܫ‬ႝǵૈໆ
ᓬᗺ ႝǵሽ਱ե ႝǵૈໆஏ
ԋዕǵሽ਱ ૈໆஏࡋଯǵ ஏࡋଯǵტ
༹ ࡋัଯ
ե༹ ტ‫ߏڮ‬ ‫ߏڮ‬ǵեԋ

ό ё ‫ ז‬ೲ ૈ ໆ ஏ ࡋ ‫ڀ‬٤೚૶Ꮻ кႝਔ౷

кႝǵૈໆ եǵ‫૶ڀ‬Ꮻ ਏᔈǵଯྕ ೷ԋε൯

લᗺ ሽ਱ၨଯ
ஏࡋեǵტ ਏ ᔈ Ъ Ԗ ᕉნΠ‫ૈ܄‬ ࡋᡏᑈᑩ

‫ڮ‬ၨอ ᕉߥୢᚒ ৡ ๞

ᆙ࡚ྣܴǵ ႝ ୏ π ‫ ڀ‬Ћᐒǵ฽૶ Ћᐒǵ฽૶ࠠ

ό ᘐ ႝ ‫ س‬ᐒǵᆙ࡚ྣ ࠠႝတǵኧ ႝတǵኧՏ࣬ ۘ ҂ ε ໆ

ЬाҔ೼
಍ǵ೯ૻ೛ ܴǵ೯ૻ೛ Տ ࣬ ᐒ ฻ ᐒ ฻ 3C ౢ ᇙ೷

ഢ ഢ 3C ౢࠔ ࠔǵႝ୏ً

10
 ᎖ႝԣԐය‫ޑ‬ว৖Ьा٬Ҕ᎖ߎឦբࣁႝཱུ‫׷‬਑Ǵҗ‫ܭ‬᎖ߎឦࢲ‫܄‬ଯᆶ‫ځ‬ҁ‫ي‬

੝‫܄‬Ǵ٬‫ځ‬ӧкǵ‫ܫ‬ႝ‫ޑ‬ਏ౗ᆶૈໆஏࡋ΢Ԗ๱ᓬ౦‫߄ޑ‬౜Ƕа౽୏ၩ‫ڀ‬Զ‫ق‬ǴҞ

߻ѱय़΢ε೽ϩًؓ٩ᙑ٬ҔӼӄࡋၨଯ‫ޑ‬ႉለ‫ᙻ܈‬ణႝԣǶՠՔᒿ๱ᕉߥཀ᛽‫ܩ‬

ᓐᆶᆘૈౢ཰‫ޑ‬ᑫଆǴЪѱ൑ሡ‫؃‬රӛᇸໆϯǵλࠠϯ‫ޑ‬ว৖ϐΠǴԖຫٰຫӭ‫ޑ‬

ႝԣቷ୘ᆶًቷӝբǴ‫׫‬Εεф౗᎖ႝԣ‫س‬಍‫ࣴޑ‬วǶฅԶǴ᏾ᡏԶ‫ق‬Ǵ᎖ႝԣԾ

ୢШаٰǴ‫زࣴځ‬ᆶ໒วπբߡόᘐӦ຾ՉǶߏයٰ࣮Ǵ᎖ႝԣς೴ᅌ‫ڗ‬жႉለǵ

ᙻణႝԣǹᒿ㰢ӄౚ࿶ᔮ‫ז‬ೲว৖ჹૈྍሡ‫ޑ؃‬όᘐቚߏаϷᕉნԦࢉ‫ޑ‬В੻ᝄख़Ǵ

ว৖‫ڀ‬Ԗଯૈໆஏࡋǵߏൻᕉტ‫ڮ‬ǵଯӼӄ‫܄‬ǵᆘՅᕉߥ‫ک‬եԋҁ‫ޑ‬Βԛႝԣӧཥ

ૈྍሦୱ‫ڀ‬Ԗख़εཀကǷᆶႉለႝԣǵᙻᙿႝԣ฻໺಍Βԛႝԣ࣬КǴ᎖ᚆηႝԣ

‫ڀ‬Ԗ‫ܫ‬ႝႝᓸଯǵૈໆஏࡋଯǵൻᕉტ‫ߏڮ‬ǵᆘՅᕉߥ฻ᡉ๱ᓬᗺǴӢԶِೲ՞Ᏽ

ΑߡឫԄႝη೛ഢǵႝ୏π‫ڀ‬ǵλࠠႝ୏ً฻ሦୱ‫ޑ‬ε೽ϩѱ൑ǷҞ߻Ǵ᎖ᚆηႝ

ԣ‫ޑ‬ᔈҔሦୱςᘉ৖Կႝ୏ًؓǵඵૈႝᆛǵ3G ೯ߞǵૐ‫ޜ‬ૐϺǵ୯ٛ฻ӭঁሦୱǴ

ԋࣁΑ 21 Шइന‫ڀ‬ᔈҔ߻ඳ‫ޑ‬ᓯૈᏔҹϐ΋Ƕ

ӧ᎖ȐᚆηȑΒԛႝԣᡏ‫س‬ύǴཱུ҅‫׷‬਑΋‫ڋࢂޔ‬ऊႝԣว৖‫ޑ‬౟ᓍ[13]Ǵ໺಍

‫ޑ‬ၸ෠ߎឦ਼ϯ‫کނ‬ᕗለᡶ฻ཱུ҅‫׷‬਑ӵ LiCoO2, LiNiO2 ‫ ک‬LiFePO4 ฻Ǵҗ‫ځܭ‬

౛ፕᓯ᎖৒ໆ‫ޑ‬ज़‫ڋ‬ςᜤаᅈ‫זى‬ೲว৖‫ޑ‬ѱ൑ሡ‫؃‬ǷӢԜǴ൨‫کפ‬໒วཥࠠଯК

ૈໆǵӼӄǵ༹ሽ‫׷ཱུ҅ޑ‬਑ࢂҞ߻ࣴ‫ޑز‬዗ᗺǷаൂ፦౷ࣁཱུ҅‫ޑ‬᎖ɡ౷Βԛႝ

ԣ[1]Ǵ‫ځ‬ύ౷ཱུ҅‫ڀ‬Ԗଯ‫ޑ‬౛ፕК৒ໆ(1675mAh / g)‫ૈک‬ໆஏࡋȐ2600Wh / kgȑǴ

Ъൂ፦౷‫ڀ‬Ԗሽ਱ե༹ǵၗྍᙦ൤ǵᕉნ϶ӳ฻ᓬᗺǴςԋࣁΠ΋жଯૈஏࡋ᎖Β

ԛႝԣ‫کزࣴޑ‬໒ว‫ޑ‬ख़ᗺǶ

კ 4 ࠠဦ 18650 ༝ࢊࠠ᎖ᚆηႝԣ޻[14]

11
2.3 ᎖ႝԣπբচ౛ᆶ੝‫܄‬
ႝԣࢂ΋ᅿҗϯᏢૈᙯඤԋႝૈ‫ޑ‬ᓯӸး࿼Ƕ᎖ᚆηႝԣҗΟঁ೽ϩಔԋǺ҅

ཱུǵॄཱུ‫ک‬ႝှ፦Ǵቶက‫ޑ‬ёкႝ᎖ႝԣࢂࡰҗ΋ঁҡᏀࣁཱུ҅Ǵ΋ঁ௦Ҕႃǵᒰ

‫܈‬ᕗለ៓‫ཱུ҅ޑ‬ǴаϷ΋ᅿҔ‫ܭ‬ၮଌ᎖ᚆη‫ޑ‬ႝှన‫܌‬ᄬԋǶ‫ܫ‬ႝਔ᎖ᚆη຾Ε҅

ཱུ‫׷‬਑‫ޑ‬ၸำћȨ൪ΕȩǴкႝਔᚆ໒‫ޑ‬ၸำћȨ൪рȩǹкႝਔ᎖ᚆη຾Εॄཱུ

‫׷‬਑‫ޑ‬ၸำћȨකΕȩǴ‫ܫ‬ႝਔᚆ໒‫ޑ‬ၸำћȨಥකȩǶკ 6 ࢂ΋ঁ᎖ႝԣк‫ܫ‬ႝ

ҢཀკǶ

კ 5 ᎖ႝԣᄬ೷ᆶк‫ܫ‬ႝᐒ‫ڋ‬

12
 ӧ‫ܫ‬ႝၸำύǴ໚ཱུೀ(Positive electrode)วғ਼ϯϸᔈǴӧϸᔈύᗋচᏊ (R1)

ஒග‫ٮ‬ႝηǴஒႝηញ‫ډܫ‬ೱௗႝၡԿཱུ҅(Negative electrode)‫਼ޑ‬ϯᏊ (R2) วғ

ᗋচϸᔈǴёҔΠӈϯᏢϸᔈԄ߄ҢǺ

­
° R1 o O1  me

at the anode
® 
(2.3)
°̄O2  me o R2 at the Cathode

வ᎖ႝԣк‫ܫ‬ႝᐒ‫ޑڋ‬ၸำϩ‫݋‬Ǵ྽ཱུ҅ߎឦᚆηᆶႝှ፦ౢғୋϸᔈԶྋှ

‫ܭ‬ႝှ፦ύǴ‫ܭ‬ൻᕉ‫܈‬ᔖ࿼ၸำύᆶॄཱུౢғᗋচϸᔈԶ‫׎‬ԋ‫ڰ‬ᡏႝှ፦໌ϯጢ

Ȑsolid electrolyte interface, SEIȑǴԜࣁ΋ঁόё଍ϸᔈǶԶᒿ๱к‫ܫ‬ႝԛኧቚуǴ

SEI ጢ཮೴ᅌಕᑈࠆࡋǴӢԶ٬ႝԣϣߔ೴ᅌ΢ϲЪ෧ϿΑࢲ‫܄‬᎖ᚆηኧໆǴ೷ԋ

ႝԣტ‫ޑڮ‬૰ଏ[15]Ƕ

வ٬Ҕచҹ΢ᆶѦӧᕉნቹៜ΢ϩ‫݋‬Ǵቹៜႝԣტ‫ޑڮ‬ЬाӢનࣁǺ

1. ྕࡋǺ྽‫ܭ‬ଯྕਔ཮٬ள᎖ᚆηႝԣϣ‫ޑ‬ႝϯᏢϸᔈೲ౗ගϲ຾Զ٬ளϣႝߔ

ߔ‫ל‬फ़եǶՠࢂ྽ྕࡋගଯਔǴΨቹៜΑୋϯᏢϸᔈ‫ޑ‬ϸᔈೲ౗ගϲǴ೷ԋႝԣ৒

ໆ‫ޑ‬૰ଏ[6, 10]ǴӕਔႝϯᏢϸᔈΨϯ‫ܭ‬ᅹႝཱུ߄य़วғǴϸᔈၸำύ཮ౢғ਻ᡏǴ

ӧଯྕଯᓸΠ೭٤਻ᡏ཮ኖ໒ႝཱུ٠Ъ೷ԋઇᚯǴӢԜჹ‫ܭ‬᎖ᚆηႝԣ‫ޑ‬ଏϯԖཱུ

ε‫ޑ‬ቹៜǶեྕΠႝԣ‫ޑ‬ф౗Ǵ৒ໆஒܴᡉΠफ़Ǵ೷ԋ‫׷‬਑඲਱‫ڙ‬ཞǴߎឦᚆηܰ

‫ܭ‬ᗋচϐόё଍ϐ૰ଏ[16]Ƕ

2. к‫ܫ‬ႝೲ౗Ǻӧଯ‫ܫ‬ႝೲ౗Π཮٬᎖ᚆη‫ޑ׷୷ܭ‬Ꮴႝࡋफ़եǴӕਔΨ཮ගϲ

ႝԣߔ‫ܫל‬ǴԶႝೲ౗ቹៜႝԣტ‫ޑڮ‬ЬाӢનࣁ᎖؈ᑈǶӧଯк‫ܫ‬ႝೲ౗ਔǴ཮

Ꮴठ᎖ᚆη‫ܭ‬ႝཱུ߄य़؈ᑈǴёૈ຾Զ೷ԋႝԣอၡ[17]Ƕ

3. к‫ܫ‬ႝుࡋǺ྽᎖ᚆηႝԣόᘐ‫ޑ‬຾Չкႝᆶ‫ܫ‬ႝำ‫ׇ‬җ‫ڰډੋ౐཮ܭ‬ᡏႝཱུ

߄य़‫ޑ‬গᚆᆶӆ؈ᑈǴฅԶຫుࡋ‫ܫޑ‬ႝஒуೲԜ௃‫׎‬ǴᏤठႝԣᓯӸႝૈૈΚ‫ޑ‬

ଏϯ[13]ǶԶၸкႝΨᏤठႝԣϣ೽ྕࡋ‫ک‬ᓸΚᡉ๱ቚуǴЇଆᐒఓ‫ࡺޑ܄‬ምᆶϡҹ

ϐ໔‫ޑ‬อၡǴ٠೷ԋႝࢬ೯ၡ΢‫ߔޑ‬ᛖǶӵ݀ၸࡋкႝΠόಖЗǴஒёᏤठႝԣᛈ

ࣆǴញ‫ܫ‬рӒᓀ‫ޑ‬ϯᏢࠔ‫਻ک‬ᡏǴԶЇଆО‫[ؠ‬15]Ƕ

13
 җ΢ॊ᎖ႝԣ੝‫܄‬Ǵႝԣܰ‫ډڙ‬ӚᅿᕉნӢηϷ٬ҔБԄԶԴϯѨਏǴᝄख़ਔ

ࣗԿ཮ԖቹៜӼӄϐဤǴ‫܌‬аࣁΑߥም੃຤‫੻៾ޣ‬Ǵ΋૓Զ‫ق‬ǴନΑًቷ‫܈‬ႝԣቷ

୘ࣣ཮ჹ‫ځ‬ౢࠔ୺Չ࣬ᜢෳ၂ᡍ᛾ٰߥ᛾ࠔ፦ѦǴ୯ሞ኱ྗύҭԖܴዴ‫ޑ‬ೕጄǴ‫ڋ‬

‫࣬ۓ‬ᜢෳ၂Б‫ݤ‬Ǵаዴߥౢࠔࠔ፦[18]Ƕӧ SAE J1798 ୯ሞ኱ྗΠǴ‫ځ‬၂ᡍ໨Ҟх

֖ᓉ৒ໆ၂ᡍ(‫ۓ‬ႝࢬ‫)ݤ‬ǵᓉ৒ໆ၂ᡍ(‫ۓ‬ф౗‫)ݤ‬ǵႝໆߥӸ၂ᡍǵкႝ‫ૈڙ܍‬Κ၂

ᡍǵঢ়ॶф౗ૈΚ၂ᡍǵ୏ᄊ৒ໆ၂ᡍ฻฻Ƕаᓉ৒ໆ၂ᡍ(‫ۓ‬ႝࢬ‫ٯࣁ)ݤ‬ǴԜෳ၂

Ҟ‫ࣁޑ‬ӧόӕ‫ܫ‬ႝ౗‫ࡋྕک‬ΠǴࡌҥ፾ӝً፶ 0 ᔈҔ٬Ҕਔ‫ૈޑ‬ໆ৒ໆǶёᔈҔӧ

዗ᆅ౛‫س‬಍ελ‫ޑ‬ሡ‫ૈک؃‬ໆ‫ޑૈ܄‬ᑔᒧෳ၂ǴаϷҔٰᡍ᛾ᇙ೷୘‫܌‬ഋॊ‫ૈ܄ޑ‬Ǵ

ӢԜ೭٤ෳ၂ሡ୺Չ 100%‫ܫ‬ႝ‫ډޔ‬ႝᓸᄒЗǴԶߚ໻ᚐ‫ۓ‬৒ໆǶ‫ځ‬ෳ၂Б‫ࣁݤ‬а

C/3 ‫ܫ‬ႝೲ౗ӧᕉნྕࡋ 25ɗΠໆෳႝԣԿᄒЗႝᓸϐ৒ໆǴೱុෳ၂Կ৒ໆᇤৡ

ӧ 2ʘаϣࣁྗǴख़ፄෳ၂ C/2 ᆶ C/1 Π‫ܫ‬ႝ‫ޑ‬৒ໆǴϷӧ 45ɗǴ0ɗϷ-20ɗόӕ

ྕࡋΠ‫ܫ‬ႝ‫ޑ‬৒ໆǶ

2.4 ᎖౷ႝԣ
ၸѐኧΜԃٰǴ᎖ᚆηႝԣ‫ૈޑ‬ໆஏࡋόᘐගଯǴቶ‫ݱ‬ᔈҔ‫ܭ‬ඵૈЋᐒ฻ሦୱǶ

ՠ᎖ᚆηႝԣሡाಁख़‫ཱུ҅ޑ‬Ȑ΋૓җ਼ϯႃ฻‫׷‬਑‫ڋ‬ԋȑٰ“ԏય”᎖ᚆηǴज़‫ڋ‬

Αႝԣૈໆஏࡋ‫ޑ‬຾΋‫؁‬ගଯǶ೭ཀ‫ښ‬๱Ǵჹፏӵߏຯᚆႝ୏ًؓ฻ሡा‫׳‬εૈໆ

ஏࡋ‫ޑ‬ᔈҔٰᇥǴ᎖ᚆηႝԣԖᗺΚόவЈǶӢԜǴࣽᏢৎॺஒҞӀ‫׫‬ӛΑ᎖ᚆη

ႝԣ‫׳‬ᠼዧ‫׷ޑ‬፦—᎖౷ႝԣ‫ي‬΢Ǵӟ‫ཱུ҅ޑޣ‬Ьाҗ౷Ȑҡ‫ݨ‬π཰༹ሽ‫ޑ‬ୋౢࠔȑ

‫ڋ‬ԋǶ౷‫“ޑ‬ᡏख़”໻ࣁႃ‫ޑ‬΋ъǴӢԜǴӕኬᡏᑈ‫ޑ‬౷ԏય‫ޑ‬᎖ᚆηኧࣁ਼ϯႃ‫ޑ‬

‫ٿ‬७Ǵ೭൩٬ள᎖౷ႝԣ‫ૈޑ‬ໆஏࡋࣁ᎖ᚆηႝԣ‫ޑ‬ኧ७ [19] Ƕ

Γॺᇡࣁ᎖౷ႝԣ಄ӝԋҁਏ੻Ǵࢂঁख़ाࣽ‫מ‬ǴёᔈҔ‫ܭ‬҂ٰёឫԄ‫ޑ‬ႝη

ౢࠔǵႝૈًؓǴΨёբࣁॶள‫ߞॺך‬ᒘ‫ޑ‬ӆғૈྍϐഢҔᓯૈ‫س‬಍Ƕҗ‫ܭ‬౛ፕ΢

ႝϯᏢ‫ޑ‬ଯ৒ໆǴ୫ୟ୶ ࣁ 1675 mAh/g ᎖౷ႝԣচ߾΢ж߄Α΋ঁԖਏ౗‫ޑ‬ᓯૈ‫س‬

಍Ƕ‫׳‬ख़ा‫ࢂޑ‬Ǵচ਑к‫ى‬ϷեԋҁԋΑ᎖౷ႝԣख़ा‫ޑ‬ᓬ༈ǶӢԜǴ᎖౷ႝԣԋ

Αஏ໣ࣴ‫ޑز‬ЬᚒǴ‫ڬ؂‬೿ԖኧጇයтౢрǶฅԶǴᒿ๱ൻᕉၸࡕܴᡉ‫ޑ‬৒ໆ෧ϿǴ
14
٬ϐค‫ݤ‬ԋࣁቶ‫ݱ‬ၮၮҔӧࣽ‫מ‬΢‫ޑ‬ႝԣǶ

࿶ၸൻᕉࡕ৒ໆΠफ़ࢂӚᅿႝԣࣁΓ೯ੰ‫ޑ‬લᗺǴЀ‫ࢂځ‬᎖ᚆηႝԣǴςԋࣁ

ቶ‫ޑزࣴݱ‬ЬᚒǴаឍܴ৒ໆӧ٬Ҕύ੃ೳ‫ޑ‬ӚᅿচӢǶӢԜǴς௢рΑ೚ӭଞჹ

᎖ᚆηႝԣ੃ೳ‫ޑ‬৒ໆ‫ޑ଺܌‬ኳࠠ[5e14]Ƕӧ Arora Ϸ‫ځ‬дᏢ‫ޑޣ‬ຑፕύǴమཱӦඔ

ॊΑ೚ӭ೷ԋ৒ໆΠफ़‫ޑ‬চӢǶ᎖ᚆη৒ໆΠफ़‫ޑ‬ኳࠠᆫขӧ೚ӭୖኧ΢Ǵ‫ٯ‬ӵྕ

ࡋǵ‫ڰ‬ᡏႝှ፦Ȑsolid electrolyte interface (SEI)ȑቫ‫ޑ‬ቚуǵࢲ‫ނ܄‬፦Πफ़ǵаϷ৒

Ꮚ‫ޑ‬෧Ͽ[12]ǶԖᜢ৒ໆ෧Ͽ‫ޑ‬ᜪ՟ᐒ‫ڋ‬Ψёૈр౜ӧ᎖౷ႝԣ΢ǶฅԶǴଞჹ᎖౷

ႝԣ࿶ၸ൳ԛؑ‫ܫ‬ൻᕉࡕ੃ೳ‫ޑ‬৒ໆǴҞ߻ᗋؒԖҺՖ‫ޑ‬ኳࠠૈჹԜໆϯϩ‫݋‬Ƕᡉ

ฅǴ᎖౷ႝԣ৒ໆ‫ޑ‬ኳࠠഢ‫ڙ‬යࣰǴӢࣁૈ୼ᡣ‫ॺך‬ໆϯКၨόӕ‫׷ޑ‬਑Ϸόӕϯ

Ꮲၮբ‫ޑ‬όӕǶ

კ 6 ᎖౷ႝԣк‫ܫ‬ႝҢཀკ

15
2-5 Ў᝘ӣ៝
Ҟ߻Ӛ஑ৎᏢ‫ޣ‬ӧႝԣ‫ޑ‬૰ଏኳࠠϩ‫݋‬Ьाёϩࣁᐒ౛ኳࠠᆶѦ੝‫܄‬ኳࠠ‫ٿ‬ε

ᜪ[20,21,22]Ǵ‫ځ‬Ьा୔ձӧ‫ܭ‬Ǵ߻‫ޣ‬๱ख़‫ܭ‬ჹႝԣϣ೽ୋϸᔈᐒ‫ڋ‬΢‫زࣴޑ‬Ǵх֖

а SEI ጢߔ௖૸ǵᚆηᐚࡋफ़եࣁᢀෳჹຝǴԶࡕ‫ޣ‬аჴᡍೕࡓрวǴ๱ख़ӧႝԣ

ൻᕉၸำύ߄౜рٰ‫ޑ‬৒ໆ૰ଏᆶϣߔ‫׎ޑ‬ԋǶ

ӧᐒ౛ኳࠠ‫ޑ‬೽ϩǴ‫ځ‬ᓬᗺࣁচ౛మධǴа‫ނ‬౛੝‫܄‬௖૸‫ޑ‬ၸำёаӄय़Αှ

ႝԣ‫ޑ‬૰ଏᐒ‫ڋ‬ǶЎ᝘[23]ਥᏵ҅ॄཱུ૰ଏᐒ‫ڋ‬Ǵவൻᕉၸำύ‫ޑ‬᎖ᚆηཞѨǵႝԣ

ϣ೽‫׷‬਑ᆭᇑ฻চ౛ࣁ୷ᘵǴࡌҥΑႝԣ SEI ጢߔቚуኳࠠǵൻᕉ૰ଏࡕ‫ޑ‬ᆄႝᓸ

ኳࠠǴฅԶҗ‫ܭ‬᎖ᚆηႝԣ၁ಒ‫ޑ‬૰ଏᐒ‫࣬ڋ‬྽ፄᚇǴၨᜤྗዴඓඝኳࠠ‫ୖޑ‬ኧǴ

ததቹៜኳࠠ՗ीᆒዴࡋЪၮᆉໆᚳεǴӢԜ΋૓όҔ‫ܭ‬ႝԣᆅ౛‫س‬಍ύǶϸϐǴ

Ѧ੝‫܄‬ኳࠠ‫ޑ‬ၮᆉ΢ၨࣁᙁൂǴЪჹ‫ܭ‬ႝԣ৒ໆ૰ଏаϷϣߔቚу฻Ѧӧ੝‫܄‬฻ᢀ

ෳჹຝϐႣෳ΢ၨࣁБߡǴҞ߻ςԖၨӭЎ᝘ගϷǴ‫ځ‬ύа Arrhenius ኳࠠࣁ୷ᘵ‫ޑ‬

௖૸ၨࣁத‫ـ‬ǴӵΠЎ‫܌‬ॊǶ

Toshiba ‫ޑ‬ЋнύගрΑ‫ځ‬ႃለ᎖ႝԣ‫ޑ‬ᓯӸტ‫ڮ‬ኳࠠǴႝԣ৒ໆཞѨ౗ࣁ[5]Ǻ
40498
Qloss 1.544 u107 exp( )t (2.4)
8.3143T
‫ځ‬ύǴT ࣁ๊ჹྕࡋǹ t ߄ҢᓯӸਔ໔ǴൂՏࣁДǶԄ(2.2)ύё࣮рࢲϯૈελ

ऊࣁ 40498(J/mol)Ǵ߄Ңрႝԣӧ૰ଏၸำύ‫ޑ‬΋໨ϯᏢϸᔈࡰ኱Ƕ

Ira Bloom ฻Ꮲ‫[ޣ‬24]຾ՉΑӧόӕᕉნྕࡋΠႝԣ૰ଏ౗‫ޑ‬ჴᡍᆶϩ‫݋‬Ǵᡍ᛾

ΑаྕࡋࣁуೲᔈΚ‫ޑ‬ႝԣ૰ଏኳࠠǴ૸ፕΑႝԣ‫࡭ߥૈ܄‬౗ᒿ๱ൻᕉਔ໔ᆶᕉნ

ྕࡋ‫ޑ‬ᜢ߯Ǻ
 Ea z
Closs A exp( )t (2.5)
RT

‫ځ‬ύǴ Closs ࣁय़ᑈКߔ‫(ל‬area specific impedance,ASI)‫ૈࢂޣ܈‬ໆǴൂՏࣁ : ‫ک‬

Wattǹ A ࣁᔕӝதኧǹ Ea ࣁࢲϯૈǴൂՏࣁขԸǹ R ࣁ਻ᡏதኧǴ t ࣁ٬Ҕტ‫ڮ‬Ǵൂ

16
Տࣁλਔǹ Z ࣁਔ໔‫ޑ‬ԛБ໨Ǵӧ΋૓‫ޑ‬௃‫ݩ‬Πё‫ ࣁڗ‬1/ 2 Ƕ A ǵ Ea /R ǵ Z ࣣё೯

ၸჴᡍኧᏵᔕӝԶளǶ

John Wang ฻Ꮲ‫[ޣ‬25]୷‫ ܭ‬Ira Bloom ฻Γ‫زࣴޑ‬ǴගрΑа Ah-throughput ࣁᡂ

ኧ‫ޑ‬ᚈӢનኳࠠǴஒ‫ܫ‬ႝుࡋ४аᚐ‫ۓ‬ႝ৒ӆ४ΕচԖ‫ޑ‬ਔ໔໨Ǵள‫ډ‬Αаྕࡋ‫ک‬

‫ܫ‬ႝໆࣁуೲᔈΚ‫ޑ‬ႝԣტ‫ڮ‬ኳࠠǴ٠ၲ‫ډ‬ӧ 20%аϣ‫ޑ‬ႣෳᇤৡǴ৒ໆཞѨ౗ࣁǺ
 Ea
Qloss =A exp( ) ˜ ( Ah ) z (2.6)
RT

‫ځ‬ύǴ Ah ࣁӧ‫ܫঁ؂‬ႝൻᕉΠႝԣ‫ܫ܌‬р‫ޑ‬ႝໆελǴ‫ځ‬ᎩୖኧࣣᆶԄ(2.4)࣬ӕǶ

Toshio Matsushima ฻Ꮲ‫[ޣ‬25]ࣴ‫ز‬Αεࠠ᎖ႝԣ‫ૈ܄ޑ‬૰ଏǴӕኬว౜৒ໆ‫ޑ‬

૰ଏᆶਔ໔և 1/ 2 ϐԛБᜢ߯Ǻ
1
Qloss =K f ˜ t 2 (2.7)

‫ځ‬ύǴ K f ࣁ߯ኧǴܺவ Arrhenius ‫ࡓۓ‬Ƕ

а Arrhenius ኳࠠࣁ୷ᘵǴHuolin Li ฻Ꮲ‫[ޣ‬26]ਥᏵႃለ᎖ႝԣϐტ‫ڮ‬ൻᕉჴ

ᡍǴගрΑаΠ Arrhenius ᘉ৖ኳࠠǺ

O /T
 mI K  f )
Qloss (a eD /T  bI E  c)nc (l e (2.8)

‫ځ‬ύǴ nc ࣁк‫ܫ‬ႝൻᕉԛኧǹ I ࣁ‫ܫ‬ႝႝࢬελǴൂՏࣁӼ୻ǹ a ǵ b ǵ c ǵ l ǵ m ǵ

f ǵ D ǵ E ǵ O ǵ K ֡ࣁୖኧǴё೯ၸჴᡍኧᏵᔕӝԶளǶ

17
2-6 λ่
ӧ຾ՉЎ᝘ཛྷ൨ࡕǴёаว౜Ҟ߻ς࿶Ԗ೚ӭࣴ‫ޣز‬ଞჹႝԣ૰ଏᐒ‫ڋ‬຾Չ࣬

྽ӭࣴ‫ز‬Ǵ٠ගрӚԄӚኬ‫ޑ‬ኳࠠ຾Չϩ‫݋‬ǶՠࢂҞ߻૰ଏኳࠠε೿ሡाᇶ՘εໆ

‫ޑ‬ჴᡍǴ٠ࡌҥ೚ӭჴᡍኧᏵǴӢԜӧεໆᕷᅥ‫ޑ‬ीᆉᇶаፄᚇ‫ޑ‬ᄽᆉ‫ݤ‬ӚጇЎ᝘

྽ύ஑‫ܭݙ‬ӚԾࣴ‫ޑز‬೽ϩǴค‫଺ݤ‬р೯ዬ‫ޑ‬КၨǶࡺҁࣴ‫׆ز‬ఈёаଞჹ೭٤ୢ

ᚒ຾Չ௖૸Ǵࡌҥ΋঺όሡाᕷᅥπբǴߡёаమཱӦඔॊрӚᜪձ᎖ႝԣൻᕉტ

‫ڮ‬аϷӚԄୖኧǴаБߡ຾ՉКၨǶჹ‫ܭ‬ቷ୘ᆶ٬Ҕ‫ٰޣ‬ᇥǴ೭٤ёૈ೿཮ӧ຾Չ

ჴሞᔈҔਔε൯ਔ໔ǵԋҁаϷ౛ှ΢‫ޑ‬ፄᚇࡋǶ

18
ಃΟകǵё᎞ࡋᆶଭёϻၸำཷፕ

ӧҁകಃ΋࿯ஒ၁ಒϟಏҁࣴ‫܌ز‬٬Ҕ‫ޑ‬ё᎞ࡋ࣬ᜢᔈҔ౛ፕǴх֖Αё᎞ࡋ‫ޑ‬

୷ҁ‫ۓ‬ကǵᒿᐒᡂኧǵ‫س‬಍ё᎞ࡋ฻౛ፕǶಃΒ࿯߾ࢂ௖૸ଭёϻၸำ࣬ᜢ‫܄‬፦Ǵх

֖‫୷ځ‬ҁࢎᄬǵ౛ፕ௢ᏤǴаϷ֎ԏ‫ރ‬ᄊ฻੝ਸ‫܄‬፦Ƕ

3.1 ё᎞ࡋ࣬ᜢ౛ፕ
ё᎞‫ۓޑ܄‬ကǺਥᏵ୯ৎ኱ྗ GB-6583 ‫ޑ‬ೕ‫ۓ‬Ǵౢࠔ‫ޑ‬ё᎞‫ࡰࢂ܄‬Ǻౢࠔӧೕ‫ۓ‬

‫ޑ‬చҹΠǵӧೕ‫ޑۓ‬ਔ໔ϣֹԋೕ‫ޑۓ‬фૈ‫ૈޑ‬ΚǶ

΋૓‫܌‬ᇥ‫“ޑ‬ё᎞‫“ࢂޑࡰ”܄‬ёߞᒘ‫“܈”ޑ‬ёߞҺ‫”ޑ‬Ƕ΋ᆵሺᏔ೛ഢǴ྽Γॺा

‫؃‬ѬπբਔǴѬ൩ૈπբǴ߾ᇥѬࢂё᎞‫ޑ‬ǹԶ྽Γॺा‫؃‬ѬπբਔǴѬԖਔπբǴ

ԖਔόπբǴ߾ᆀѬࢂόё᎞‫ޑ‬ǶჹౢࠔԶ‫ق‬Ǵё᎞‫܄‬ຫଯ൩ຫӳǶё᎞‫܄‬ଯ‫ޑ‬ౢ

ࠔǴёаߏਔ໔҅தπբȐ೭҅ࢂ‫܌‬Ԗ੃຤‫ޣ‬ሡाள‫ޑډ‬ȑ
ǹவ஑཰‫ٰࡋف‬ᇥǴ൩ࢂ

ౢࠔ‫ޑ‬ё᎞‫܄‬ຫଯǴౢࠔёаคࡺምπբ‫ޑ‬ਔ໔൩ຫߏǶᙁൂ‫ޑ‬ᇥǴ੟က‫“ޑ‬ё᎞‫”܄‬

ࢂౢࠔӧ٬Ҕය໔ؒԖวғࡺም‫܄ޑ‬፦Ƕ‫ٯ‬ӵ΋ԛ‫ݙ܄‬৔ᏔǴӧ٬Ҕ‫ޑ‬ਔ໔ϣؒԖ

วғࡺምǴ൩ᇡࣁࢂё᎞‫ޑ‬ǹӆӵࢌ٤΋ѿวғࡺም൩όૈӆԛ٬Ҕ‫ޑ‬ౢࠔǴВӀ

ᐩᆅ൩ࢂ೭ᜪࠠ‫ޑ‬ౢࠔǴ΋૓ཞᚯΑѝૈ‫׳‬ඤཥ‫ޑ‬Ƕ

வቶက΢‫ۓ܌‬က‫“ޑ‬ё᎞‫ࡰࢂ”܄‬٬Ҕ‫ޣ‬ჹౢࠔ‫ޑ‬ᅈཀำࡋ‫܈‬ჹҾ཰‫ߞޑ‬ᒘำࡋǶ

Զ೭ᅿᅈཀำࡋ‫ߞ܈‬ᒘำࡋࢂவЬᢀ΢ٰղ‫ޑۓ‬ǶࣁΑჹౢࠔё᎞‫଺܄‬р‫ڀ‬ᡏ‫ۓک‬

ໆ‫ޑ‬ղᘐǴёஒౢࠔё᎞‫܄‬ёа‫ۓ‬ကࣁӧೕ‫ޑۓ‬చҹΠ‫ک‬ೕ‫ޑۓ‬ਔ໔ϣǴϡᏔҹȐౢ

ࠔȑ
ǵ೛ഢ‫سޣ܈‬಍ᛙ‫ֹۓ‬ԋфૈ‫ޑ‬ำࡋ‫܄܈‬፦Ƕ‫ٯ‬ӵǴًؓӧ٬ҔၸำύǴ྽ࢌঁ

႟ҹวғΑࡺምǴ࿶ၸঅ౛ࡕϝฅૈ୼ᝩុᎯᎭǶ

ౢࠔჴሞ٬Ҕ‫ޑ‬ё᎞‫܄‬ћ଺πբё᎞‫܄‬Ƕπբё᎞‫܄‬Ξёϩࣁ‫ڰ‬Ԗё᎞‫ک܄‬٬Ҕ

ё᎞‫܄‬Ƕ‫ڰ‬Ԗё᎞‫ࢂ܄‬ౢࠔ೛ीᇙ೷‫ޣ‬Ѹ໪ዴҥ‫ޑ‬ё᎞‫܄‬Ǵջࡪྣё᎞‫܄‬ೕჄǴவ

চ‫׷‬਑‫ک‬႟೽ҹ‫ޑ‬ᒧҔǴ࿶ၸ೛ीǵᇙ೷ǵ၂ᡍǴ‫ډޔ‬ౢࠔрౢ‫ޑ‬Ӛঁ໘ࢤ‫܌‬ዴҥ

19
‫ޑ‬ё᎞‫܄‬Ƕ٬Ҕё᎞‫ࡰࢂ܄‬ςғౢ‫ޑ‬ౢࠔǴ࿶ၸхးǵၮᒡǵᓯӸǵӼးǵ٬Ҕǵ

ᆢঅ฻Ӣનቹៜ‫ޑ‬ё᎞‫܄‬Ƕ

ё᎞ࡋຑ՗ࢂ߈൳Μԃٰᑫଆ‫ޑ‬΋ߐπำ‫ೌמ‬Ǵ‫ྍځ‬ଆ‫ ܭ‬1940 ԃಃΒԛШࣚε

Ꮿය໔ቺ୯຾ՉОጂѨᇤϷӼӄ‫زࣴޑ܄‬ǶόΦࡕǴऍैଞჹଯࡺም౗‫ޑ‬Ꮿᐒႝη

೛ഢǴ৖໒ΑԖ‫س‬಍Ӧё᎞ࡋࣴ‫ز‬Ǵ٠ว౜ΑࡺምЬӢٰԾ‫ޜ੿ܭ‬ᆅǴ٠ଞჹ੿‫ޜ‬

ᆅ‫ޑ‬ѨਏচӢǴӵႝ਻ǵᐒఓ฻੝‫ִ܄‬๓‫ׯ‬຾ǴӕਔҭԵໆ᏾ঁးഢ‫س‬಍᏾ӝ‫ޑ‬ୢ

ᚒǶനಖ٣ჴ᛾ܴǴ࿶ၸΑ‫ׯ‬๓Ǵ੿‫ޜ‬ᆅ‫ࡺޑ‬ም౗ܴᡉ෧ϿǶ೭ࢂπำў΢΋໨ख़

ा‫ޑ‬ԋ൩ǴၸѐΓॺයఈҔӚᅿБԄᆢៈ‫ׯ܈‬๓ౢࠔࠔ፦Ǵՠ۳۳ပΕ೏୏‫ׯ‬๓‫ޑ‬

࿭ՀǴ٬ளౢࠔค‫ݤ‬วචচԖႣයϐ‫ૈ܄‬Ƕ‫ځ‬চӢٰԾ‫ܭ‬೛ी‫ޣ‬۹ౣΑΓࣁᏹբǵ

ᕉნӢηǴౢࠔԴϯ฻ѦӧӢન‫ޑ‬ቹៜǴջߡ‫ޕ‬ၰǴҭલЮ಍ी౛ፕᡍ᛾೭٤Ӣન

ᆶࡺምϐ໔‫ޑ‬ᜢ߯Ƕ྽ࣽᏢৎϷπำৣॺሦ৴‫ډ‬ё᎞ࡋ౛ፕഖ‫ى‬аჹ౜жπ཰ౢғ

ವεቹៜǴ‫زࣴ࣬ݾ‬ΠǴё᎞ࡋπำၱԋࣁ΋ߐཥᑫ‫ޑ‬ᏢୢǴԜࡕё᎞ࡋࣴ‫ز‬ሦୱ

‫ۯ‬՜Կႝηౢࠔǵᐒఓᄬҹǵᏹբ೬ᡏǵ࿶ᔮᏢǴࣗԿх֖΢ॊϐεࠠፄᚇ‫س‬಍Ǵ

‫ى‬аΑှё᎞ࡋϐख़ा‫܄‬Ƕ

3.2 ё᎞ࡋᙁϟ
ё᎞ࡋΏ٬Ҕ‫ޣ‬ჹౢࠔߞᒘ‫ޑ‬ໆϯૈΚǴਥᏵ‫ځ‬ሡ‫؃‬όӕǴໆϯࡰ኱ёૈࣁᐒ౗ǵ

٬Ҕਔ໔ǵ٬Ҕԛኧ฻฻Ƕֹ᏾‫ޑ‬ё᎞ࡋ‫ۓ‬ကǴᔈ၀֖Ѥ໨చҹ[27]

1. Ѩਏ‫ޑ‬ඔॊǺѨਏջౢࠔ҂ૈวචႣ‫ۓ‬ᐒૈϐ‫ރ‬ᄊǶёϩࣁࡺምǵόᛙ‫܈ۓ‬ф

૰ଏǶ

2. යఈ‫ޑ‬ტ‫ڮ‬Ǻࣚ‫ۓ‬ё᎞ࡋѸ໪Ӄዴ‫ۓ‬ౢࠔයఈ‫ޑ‬ਔ໔Ǵऩ٬Ҕਔ໔ຬၸౢࠔ‫ޑ‬

Ҕტ‫ڮ‬ය (Useful life period) Ǵ߾ё᎞ࡋ‫ޑ‬ा‫ߡ؃‬คཀကё‫ق‬Ƕ

3. ᕉნ‫ޑ‬ቹៜǺҺՖౢࠔӧ٬Ҕၸำύ೿όᘐ‫ډڙ‬ϣѦᕉნቹៜǴத‫ޑـ‬Ԗႝᓸ

ႝࢬǵྕࡋǵᔈΚǵᔸࡋǵለᡵ‫܄‬฻฻ǴӢԜ೛ीౢࠔਔǴਥᏵ٬Ҕచҹफ़եᕉნ

ቹៜӢનǴҭ‫ࢂ܈‬மϯౢࠔӧ੝‫ۓ‬ᕉნΠϐऐ‫܄ڙ‬Ǵ೿Ԗշ‫ܭ‬Ԗਏගଯё᎞ࡋǶ

4. ᐒ౗‫ޑ‬ϩѲǺё᎞ࡋࢎᄬࢂаᐒ౗಍ीࣁ‫ځ‬ਡЈཷ‫ۺ‬ǴӢԜஒ‫ܜ‬ຝኳጋ‫ޑ‬ё᎞
20
 ࡋаమධ‫ޑ‬ᐒ౗ॶ߄ҢǴёаܴዴբࣁπำ೛ी΢‫ୖޑ‬ԵǶ

3.3 ё᎞ࡋኧᏢኳࠠཷፕ
ीਔࠠౢࠔதҔё᎞ࡋ‫ڄ‬ኧٰ߄Ңϐ[28]Ǵ‫ځ‬ኧᏢࠠԄӵΠ

R( t ) P r T{t t (3.1)

‫ځ‬ж߄ཀကࣁȨӧਔ໔ t ϣǴ‫س‬಍‫܈‬ϡҹૈ୼҅தπբ‫ޑ‬ᐒ౗ȩ
Ǵ‫ځ‬ύ T ࣁᒿᐒᡂኧǴ

߄Ң‫س‬಍‫܈‬ϡҹ҅தπբ‫ޑ‬ᕴਔ໔Ǵඤ‫ق‬ϐǴёаຎࣁ‫س‬಍‫܈‬ϡҹϐტ‫ڮ‬Ƕё᎞ࡋ

‫ڄ‬ኧ‫ڀ‬ഢаΠΟᅿ੝‫܄‬Ǻ

1. R(0) 1 Ǵӧ t 0 ਔǴ‫ځ‬ё᎞ࡋࣁ 1

2. lim R(t ) 0 Ǵӧਔ໔ᖿ߈‫ܭ‬คጁεਔǴ‫ځ‬ё᎞ࡋࣁ 0

x of

3. 1 t R(t ) t 0 Ǵ‫ځ‬ё᎞ࡋॶϟ‫ ܭ‬0 ‫ ډ‬1 ϐ໔Ƕ

ӢჴᡍኧᏵёૈࣁೱុࠠ‫܈‬ᚆණࠠၗ਑Ǵᜤаࣚ‫܌ۓ‬Ԗ٣ҹϐᐒ౗ॶǴࡺ௦Ҕ

Kolmogorov ᐒ౗Ϧ೛ٰೕጄᐒ౗‫ڄ‬ኧǴ‫ځ‬ύ ( P , ‚, : ) ࣁ΋ᐒ౗‫ޜ‬໔ (Probability

Space)Ǵ٠ᅈ‫ى‬Πӈచҹ

P( A) t 0, A ‚ (3.2)

P(:) 1 (3.3)
n n
Ai  ‚; and Ai ˆ Aj I , i z j Ÿ P(
i 1
Ai ) ¦ P( A )
i 1
i (3.4)

΋૓ኬҁ‫ޜ‬໔ : ΜϩፄᚇǴࡺதஒ : ‫׫‬ቹ‫ډ‬໣ӝ x ᙁϯϐǶ‫ۓ‬က X ࣁ : ΢‫ޑ‬ᒿᐒᡂኧǶ

ऩ‫ڄ‬ኧ X : : o R ᅈ‫ى‬Πӈచҹ

X  R, {Z | X (Z) d x}‚ (3.5)

ऩ X (:) ࣁ΋ёኧ໣ӝ (Countable Set) Ǵ߾ᆀ X ࣁᚆණ (Discrete) ᒿᐒᡂኧǶзǴ߾

ᆀ p( x) ࣁ X ϐᐒ౗፦ໆ‫ڄ‬ኧ (Probability Mass Function, PMF) ǹ٠ᅈ‫ى‬аΠచҹ

p ( x) P({Z | X (Z) x}) (3.6)

p( x) t 0, x 0,1, 2,... ! (3.7)

21
 f

¦ p ( x)
x 0
1 (3.8)

ԜѦǴᚆණᒿᐒᡂኧ X ϐයఈॶ ( P ) ᆶᡂ౦ኧ ( V 2 ) ‫ۓ‬ကӵΠ

n
P E( X ) ¦ x ˜ p( x )
i 1
i i (3.9)
n
V 2 Var ( X ) ¦ ( x P )
i 1
i
2
˜ p( xi ) (3.10)

X (:) ࣁ΋όёኧ໣ӝ (Uncountable Set) Ǵ߾ᆀ X ࣁೱុ (Continuous ) ᒿᐒᡂ

ኧǶзǴ߾ᆀ F ( x) ࣁ X ϐಕᑈϩଛ‫ڄ‬ኧ (Cumulative Distribution Function, CDF) Ƕ

ӆჹ F ( x) ༾ϩǴջёள

! ! F ( x) PZ( { ZX
| d( (3.11)

d
f ( x) {F ( x)} (3.12)
dx
߾ f ( x) ᆀࣁ X ϐᐒ౗ஏࡋ‫ڄ‬ኧ (Probability Density Function, PDF) ǴЪ PDF ᅈ‫ى‬а

ΠచҹǺ

f ( x) t 0,  f  x  f (3.13)
f
³
f
f ( x)dx 1 (3.14)

ԜѦǴೱុᒿᐒᡂኧ X ϐයఈॶᆶᡂ౦ኧϩձ‫ۓ‬ကӵΠ
f
P E( X ) ³ f
x ˜ f ( x)dx (3.15)

f
V 2 Var ( X ) ³
f
( x  P )2 ˜ f ( x)dx (3.16)

22
ӧԜ੝ձϟಏ൳ᅿೱុ‫܄‬ϩଛύख़ा‫ޑ‬ϩଛǺ

1. தᄊϩଛ (Normal Distribution) ǺΞᆀբଯථϩଛ (Gaussian Distribution) Ǵ೚

ӭ಍ी௢ፕதଷ‫҆ۓ‬ᡏࣁதᄊϩଛǴ‫ځ‬ᐒ౗ஏࡋ‫ڄ‬ኧᆶಕᑈϩѲ‫ڄ‬ኧࣁǴऩ

ª ( x  P )2 º
« »
1 2V 2 »¼
PDF f ( x) ( )e «¬ , (f  x  f) (3.17)
2SV

ª ( t  P )2 º
1 f « » xP
CDF F ( x) ( ) ³ e ¬« 2V 2 ¼»
dt )( ) (3.18)
2SV f V

P 0 Ъ V 2 1 Ǵ߾ᆀբ኱ྗதᄊϩଛǶ

2. ࡰኧϩଛ (Exponential Distribution) ǺࡰኧϩଛதҔ‫ۓڰܭ‬Ѩਏ౗‫ޑ‬ౢࠔტ‫ڮ‬ϩ

ѲǴΨ൩ࢂౢࠔѨਏЬाࢂᒿᐒཀѦӢનǴԶᆶԴϯคᜢǴ‫ځ‬ᐒ౗ஏࡋ‫ڄ‬ኧᆶಕᑈ

ϩѲ‫ڄ‬ኧࣁ

PDF f (t ) OeOt (0 d t d f) (3.19)

³ Oe
 Ou
! CDF F (t ) du 1  e Ot (3.20)
0

3. ॡդϩଛ (Weibull Distribution) ǺॡդϩଛதᔈҔ‫ܭ‬ႝηǵᐒఓ฻πำ࣬ᜢѨ

ਏਔ໔‫ޑ‬ኳԄǶԖ΋ǵΒǵΟᅿୖኧǴх֖Α‫ୖރ׎‬ኧ (Shape Parameter) ǵЁࡋୖ

ኧ (Scale Parameter) ǵߐᘖୖኧ (Threshold Parameter) Ǵ‫ځ‬ύ‫ୖރ׎‬ኧࢂനख़ा‫ޑ‬

ୖኧǴѬ،‫ۓ‬ΑஏࡋԔጕ‫୷ޑ‬ҁ‫ރ׎‬ǴᒧҔ፾྽‫ୖރ׎ޑ‬ኧࣗԿёа߈՟‫ࡰܭ‬ኧϩ

Ѳǵதᄊϩթ฻‫ځ‬дஏࡋԔጕǹЁࡋୖኧ،‫ۓ‬Α‫ڄ‬ኧკ‫ޑ׎‬ελǴӧόቹៜ‫ޑރ׎‬

௃‫ݩ‬Π‫ܫ‬ε‫܈‬ᕭλǴӕਔΨ،‫ۓ‬Α੝ቻტ‫( ڮ‬Characteristic Life) ǹߐᘖୖኧࢂࡰϩ

Ѳ‫ ک‬0 ϐ໔‫࣬ޑ‬ৡՏ౽Ǵ‫܌‬ԖኧᏵ೿Ѹ໪ε‫ߐܭ‬ᘖॶǴჹ‫ܭ‬ஏࡋԔጕ‫ڄ‬ኧԶ‫ق‬Ǵߐ

ᘖୖኧё௓‫ځڋ‬НѳՏ࿼Ƕᒿ๱Οᅿୖኧ‫ޑ‬ҺཀᡂඤǴॡդϩѲё፾Ҕ‫ܭ‬ӭᅿ‫ࡺޑ‬

23
ምኳԄǴ‫ځ‬ᐒ౗ஏࡋ‫ڄ‬ኧࣁᆶಕᑈϩѲ‫ڄ‬ኧࣁ

E x  T E 1 ( xDT )E
PDF f ( x) ( ) e ,( x ! 0) (3.21)
D D
x T
( )
E
CDF F ( x) 1  e ) (3.22)

‫ځ‬ύ D ࣁ‫ୖރ׎‬ኧǹ E ࣁЁࡋୖኧǹ T ࣁߐᘖୖኧ

4. ჹኧϩଛ (Logarithmic Distribution) Ǻჹኧϩଛӧπำ΢த٬Ҕჹኧதᄊϩଛ

(Lognormal Distribution) аϷჹኧ-Տ࿼-Ёࡋϩଛ (Log-Location-Scale Distribution)

‫ٿ‬ᅿǶऩᒿᐒᐒᡂኧ X ‫ڗ‬ჹኧࡕܺவ΋தᄊϩଛǴ߾ᆀԜϩଛࣁჹኧதᄊϩଛǴ‫ځ‬ᐒ

౗ஏࡋ‫ڄ‬ኧᆶಕᑈϩѲ‫ڄ‬ኧࣁ

ª (ln x u )2 º
« »
1 «¬ 2V
2
»¼
PDF f ( x) ( )e (3.23)
2SV x

ª (ln x  u ) º
CDF F ( x) I « »¼ (3.24)
¬ V
logT u  VH Կ‫ܭ‬ჹኧ-Տ࿼-Ёࡋϩଛࢂҗ Lawless ӧ 2003 ‫܌‬ගр‫ޑ‬Ǵ‫ۓځ‬ကӵ

ΠǴऩଷ೛ౢࠔტ‫ ڮ‬T ϐᐒ౗ϩଛᅈ‫ى‬

(3.25)

߾ᆀԜϩଛࣁჹኧ-Տ࿼-ЁࡋϩଛǴӕਔ၀ϩଛᅈ‫ى‬аΠ‫ۓ‬౛ऩ PDF f ( x) Ъ

Y g ( X ) Ǵ‫ځ‬ύ g ࣁൂፓ‫ڄ‬ኧ (Monotone function) Ǵ߾

d 1
PDF g ( y) f ( g 1 ( y)) | g ( y) | (3.26)
dy
٩Ԝ‫ۓ‬౛ǴёளΠӈ่݀Ǻ
T
i. ऩy ( ) E ࣁᚈୖኧ Gamma ϩଛǴ߾ T ࣁΟୖኧ Gamma ϩଛ
D
ln T  u
ii. ऩ ࣁ኱ྗதᄊϩଛǴ߾ T ࣁჹኧதᄊϩଛ
V

24
3.4 ‫س‬಍ё᎞ࡋ
ౢࠔ‫س‬಍ࢂҗϣ೽Ӛ႟ಔҹ٩Ᏽ੝‫ۓ‬БԄಔӝԶԋǴӚ೽ҹ࣬ϕଛӝၮբаֹ

ԋႣයфૈϐᆕӝᡏǴ‫ځ‬ё᎞ࡋ‫ڗ‬،‫ܭ‬႟ಔҹаϷಔӝБԄϐё᎞ࡋǶࡌᄬ‫س‬಍ё

᎞ࡋਔ΋૓ᒥൻаΠ୷ҁଷ೛

1. ‫س‬಍ᆶӚ೽ҹϐ‫ރ‬ᄊ໻Ԗ҅த‫܈‬Ѩਏ‫ٿ‬ᜪǶ

2. Ӛ೽ҹϐ҅த‫܈‬Ѩਏ‫ރ‬ᄊࢂ۶Ԝᐱҥ‫ޑ‬Ƕ

3.5 ଭёϻၸำᙁϟ
ଭёϻၸำ‫ࢂۺཷޑ‬җ߮୯ኧᏢৎ Andrey Markov Ծ 1906 ԃගрǴӧ 1936 ԃ

࿶җ߮୯ኧᏢৎ Kolmogorov ௢ቶࡕǴቶ‫ݱ‬ၮҔӧ೚ӭሦୱ΢Ƕ‫ځ‬ཀကࢂӧ‫ރ‬ᄊ‫ޜ‬

໔ύǴவࢌ΋‫ރ‬ᄊᙯ౽‫ډ‬ќ΋‫ރ‬ᄊ‫ޑ‬΋ঁኧᏢ‫س‬಍ǶѬࢂ΋ঁᒿᐒၸำǴЪό‫ڀ‬Ԗ

૶Ꮻ‫܄‬፦ǴΨ൩ࢂᇥǴΠ΋ঁ‫ރ‬ᄊ໻٩ᒘ‫ܭ‬྽߻‫ރ‬ᄊǴԶᆶϐ߻ၸำคᜢǴԜ΋໻

Ԗ࣬ᎃ୔໔཮ϕ࣬ቹៜϐ‫܄‬፦ߡᆀբଭёϻ‫܄‬፦ (Markov Property) Ǵ‫ځ‬ᜢ߯ёҔΠ

ӈϦԄ߄ၲ[29]

Pr{X n1 j | Xn i, X n1 in1 ,..., X1 i1 , X 0 i0 } Pij (3.32)

‫ځ‬ύ X 0 , X1 ,..., X n1 ж߄‫ރ‬ᄊᒿᐒᡂኧǴi0 , i1 ,..., in1 ж߄Ӛ໘ࢤ‫ރޑ‬ᄊǴԶ Pij ջж߄྽

߻‫ރ‬ᄊࣁ i ǴௗΠٰ‫ރ‬ᄊᡂԋ j ‫ޑ‬ᙯ౽ᐒ౗ǴӢԜ Pij Ξᆀբᙯ౽ંତ ( Transition

Matrix) Ǵஒ Pij ቪԋંତࠠԄёள

ª P11 P12 P11kk º

« P22kk »»
Pijj « P21 P22
« » (3.33)
« »
¬ Pk1 Pk 2 Pkkk ¼

k ࢂ‫܌‬Ԗ‫ރ‬ᄊ‫ޑ‬ёૈኧǶќѦǴંତύ‫؂‬΋ӈ೿ёຎࣁ΋ӈӛໆ u Ǵ‫؂‬΋ӈӈӛໆ֡

ࣁᐒ౗ӛໆǴ٠‫ڀ‬ԖΠӈ‫܄‬፦

25
 °ui t 0, i 1, 2,..., k
­
®
°̄¦ ui 1
(3.34)

ਥᏵԄ (3.26) ǴёճҔ Chapman-Kolmogorov equation ள‫ډ‬ᜢ߯ԄǺ

p m n p m˜ p (3.35)

p m ࣁ࿶ၸ m ‫ރ؁‬ᄊϐᙯ౽ંତǴ p n ࣁӆ࿶ၸ n ‫ރ؁‬ᄊϐᙯ౽ંତǴҗԜϦԄё‫ޕ‬Ǵ

Ӛ‫ރ‬ᄊϐᙯ౽ᐒ౗‫ڀ‬Ԗ४Ꮘಕᑈϐ‫܄‬፦Ƕ! ! ਥᏵԜ‫܄‬፦Ǵё௢Ꮴр

Xi Pijn = X j (3.36)

‫ځ‬ύ X i ࣁ΋ӈӛໆǴᆀࣁ߃‫ރۈ‬ᄊӛໆ (Initial Stare Vector) Ǵӛໆύ‫؂‬΋ϡનж

߄Ӛ‫ރ‬ᄊวғϐᐒ౗ॶǹԶ X j ࣁ΋ՉӛໆǴ‫ځ‬ཀကࣁ࿶ၸ n ԛᙯ౽ Pij ࡕ‫܌‬ளϐӚ

‫ރ‬ᄊᐒ౗ॶǶ

26
3.6 ଭёϻኳࠠϐ੝ਸ‫܄‬፦

з p ࣁ҅ೕଭёϻၸำϐᙯඤંତǴ߾྽ n ୼εਔǴંତ p n ஒᖿ߈‫ܭ‬΋ঁ‫ۓڰ‬

ંତ

pn
! ! ! ! ! ! ! ! ! ! ! l i m T (3.37)
n of

Ԝਔંତ T ϐ‫؂‬΋ӈ֡࣬฻ǴЪ฻‫ܭ‬΋ঁᐒ౗ӛໆ t ǴԜ΋ᐒ౗ӛໆǴᆀբଭёϻၸ

ำ‫ޑ‬ᛙ‫ۓ‬ϩଛ ( Stationary Distribution) ǶԜѦǴӧଭёϻၸำύǴ྽٣ҹ΋ѿ຾Ε

ࢌᅿ‫ރ‬ᄊࡕǴߡ཮ଶᎫӧ၀‫ރ‬ᄊϣǴЪόӆᡂ୏Ǵ߾ᆀԜ΋‫ރ‬ᄊࣁ֎ԏ‫ރ‬ᄊ

( Absorbing State ) Ƕऩଭёϻၸำ‫ڀ‬ԖаΠ‫ٿ‬ᅿ੝‫܄‬Ǻ

1. ԿϿӸӧ΋ᅿ֎ԏ‫ރ‬ᄊǶ

2. ٣ҹӧҺՖߚ֎ԏ‫ރ‬ᄊǴ࿶ၸԖज़යϐࡕǴ೿཮ၲ‫֎ډ‬ԏ‫ރ‬ᄊǶ

߾၀ଭёϻၸำΞᆀբ֎ԏଭёϻၸำ ( Absorbing Markov Process)ǶԶӧଭёϻ

߃‫ރۈ‬ᄊӛໆύǴऩᐒ౗ϼե‫ځ܈‬дӢનట࣪ౣࢌ٤‫ރ‬ᄊǴ߾ёаҔ‫ځ‬д‫ރ‬ᄊ֎ԏ

ϐǶ

27
ಃѤകǵଭёϻၸำኳࠠࡌᄬ

ႝԣচ౛ᆶଭёϻၸำ֡ӧ߻കբΑ၁ᅰ‫ޑ‬ϟಏǴటࡌᄬႝԣ୏ᄊ‫ܫ‬ႝኳࠠۘ

ሡ೸ၸଭёϻၸำࡌҥኳࠠ଺຾΋‫ޑ؁‬Кၨϩ‫݋‬ǴӕਔΨѸ໪ჹଭёϻၸำύӚঁ

‫ރ‬ᄊᆶᐒ౗଺рܴዴ‫ۓ‬ကǶӧ᎖౷ႝԣύǴ‫؂‬ԛ‫ޑ‬к‫ܫ‬ႝൂᐱᚆηࣣᗧឦ‫ރܭ‬ᄊ‫ޜ‬

໔ϐύǴ٠Ъ‫ܭ‬к‫ܫ‬ႝၸำύ಄ӝ‫ރ‬ᄊϐ໔ᙯඤϐᒿᐒၸำǴӢԜҁፕЎኳࠠࢂ୷

‫ܭ‬ଭёϻၸำ[28]ȐMarkov processȑ‫ۯ܌‬՜ࡌᄬԶԋǴଭёϻၸำਥᏵ᎖౷ႝԣ่

ᄬǴඔॊႝԣӧ࿶ᐕ‫؂‬΋ԛк‫ܫ‬ႝൻᕉࡕǴႝ৒ໆᡂϯǶ೭໨౛ፕቶ‫ޑݱ‬ၮҔӧ่

ᄬғ‫ނ‬Ꮲ‫ޑ‬ኳࠠǴёҔٰᓬϯး࿼Ϸႝ୏ً‫ྍૈޑ‬ᆅ౛Ǵ‫ࢂ܈‬Ҕаှ،ૈྍ‫ٮ‬ᔈύ

‫ޑ‬ᓬϯୢᚒǴӃ߻ΨҔٰඔॊႝԣӧး࿼Ϸႝ୏ًύǴ୺Չૈྍᆅ౛ᓬϯਔၶ‫ޑډ‬

૰ଏၸำǶ೭٤ኳࠠ‫ࠠڂ‬ӦӃଷ‫ۓ‬Α੝‫ޑۓ‬ϯᏢ‫س‬಍ǴԶ૰ଏ‫ޑ‬ኳࠠ൩ࢂ୷‫ܭ‬Ԝଷ

೛[29,30]Ƕ

ҁകϩࣁΟঁ೽ϩǴಃ΋೽ϩǴࣁଞჹ᎖౷ႝԣϐЎ᝘‫ۓ‬ကрଭёϻኳ‫ރ׎‬ᄊǴӆ

‫ۓޣ‬ကӚঁ‫ރ‬ᄊϐ໔‫ޑ‬ᙯ౽ᐒ౗ǹಃΒ೽ϩǴᙖҗኳࠠࡌᄬ‫ރ‬ᄊаϷᙯ౽ᐒ౗аࡌ

ᄬଭёϻၸำ΋໘ᙯ౽ંତǴ٠‫ۓ‬ကӚ‫ރ‬ᄊϐ߃‫ۈ‬ᐒ౗Ǵीᆉр‫؂‬΋ԛк‫ܫ‬ႝࡕഭ

Ꭹϐႝ৒ໆǶಃΟ೽ϩǴҗ‫ܭ‬ଭёϻၸำ֖Ԗόዴ‫܄ۓ‬Ǵ௢ᆉр‫؂‬΋ԛк‫ܫ‬ႝࡕ‫ޑ‬

όዴ‫܄ۓ‬ᡂϯǶ

28
4.1 ଭёϻኳࠠࡌᄬ
ҁፕЎ‫܌‬௖૸ϐଭёϻၸำኳࠠёୖྣკ 8Ǵх֖Ѥᅿ‫ރ‬ᄊឦ‫ܭ‬Οঁឦ‫܄‬Ƕ२

ӃǴஒ‫ٿ‬ᅿࢲ៌‫ރ‬ᄊ‫ۓ‬ကԋၨࣁᛙ‫ ޑۓ‬Active1(ୟଵ )‫ރ‬ᄊаϷၨόᛙ‫ ޑۓ‬Active2(ୟଶ )

‫ރ‬ᄊǴӧԜ‫ރ‬ᄊΠ᎖ᚆηܰวғк‫ܫ‬ႝѦϐϯᏢᡂϯ೷ԋ؈ᐘǴ‫ٿ‬ᅿࢲ៌‫ރ‬ᄊ೿ஒ

ჹႝԣႝ৒ໆౢғଅ᝘ǹ‫ځ‬ԛ‫ۓ‬ကόࢲ៌‫ރ‬ᄊ Inactiveሺ୧ ሻǴӧԜ‫ރ‬ᄊΠ࿶җк‫ܫ‬ႝ

ൻᕉၸำ཮೴ᅌᐟࢲᙯᡂԋၨࣁᛙ‫ ޑۓ‬Active1(ୟଵ )ǹനࡕ‫ۓ‬ကԝΫ‫ރ‬ᄊ Dead(ୢ )Ǵ

Ԝ‫ރ‬ᄊࣁ֎ԏ‫ރ‬ᄊٰ߄Ң᎖ᚆηςค‫ݤ‬ᙯᡂӣࢲ៌‫ރ‬ᄊǶ‫ۓ‬က X ࣁ‫ރ‬ᄊϐᡂኧǴЪ

x(n)߄Ңӧಃ n ԛк‫ܫ‬ႝࡕ᎖ᚆη‫܌‬ӧϐ‫ރ‬ᄊǴ‫ܭ‬Ѥᅿ‫ރ‬ᄊύ‫ޑ‬ᙯ౽ᐒ౗߾ϩձ߄

Ңࣁ

P(x(n+1)=d | x(n)=a1)=ୟଵ՜ୢ

P(x(n+1)=a1 | x(n)=a1)=ୟଵ՜ୟଵ = 1-ୟଵ՜ୢ

P(x(n+1)=d | x(n)=a2)=ୟଶ՜ୢ (4.1)

P(x(n+1)=a1 | x(n)=a1)=ୟଵ՜ୟଵ = 1-ୟଵ՜ୢ

P(x(n+1)=a1 | x(n)=i)=୧՜ୟଵ

P(x(n+1)=i | x(n)=i)=୧՜୧ =1-୧՜ୟଵ

P(x(n+1)=d | x(n)=d)=1

კ 7 ଭёϻၸำኳࠠҢཀკ

29
4.2 ᙯ౽ંତᆶᔈҔ
٩Ᏽ 4.1 ‫܌‬ॊϐኳࠠаϷᙯ౽ᐒ౗‫ॺך‬ёаளаΠંତ

‫܉܁‬૚ ୟଵ՜ୟଵ Ͳ Ͳ ୟଵ՜ୢ

‫܉܉܁‬૛ Ͳ ୟଶ՜ୟଶ Ͳ ୟଶ՜ୢ
‫ ܑ܁ =۾‬൦ ୧՜ୟଵ
ġ
Ͳ ୧՜୧ Ͳ
൪ (4.2)
‫܌܁‬ Ͳ Ͳ Ͳ ͳ

٠Ъ‫ۓ‬ကӧୟଵ ǡ ୟଶ ǡ ୧ ǡ ୢ ‫ۈ߃ޑ‬ᐒ౗ϩձࣁˆୟଵ ሺͲሻ, ˆୟଶ ሺͲሻ, ˆ୧ ሺͲሻ, ˆୢ ሺͲሻ߾࿶ၸ n ԛк

‫ܫ‬ႝൻᕉࡕ‫ܭ‬Ӛঁ‫ރ‬ᄊϐᐒ౗ஒࣁˆୟଵ ሺ݊ሻ, ˆୟଶ ሺ݊ሻ, ˆ୧ ሺ݊ሻ, ˆୢ ሺ݊ሻǴӵΠ߄Ң

ˆୟଵ ሺሻ ˆୟଵ ሺͲሻ

ˆ ሺሻ ˆ ሺͲሻ
൦ ୟଶ ൪=  ୬ ൦ ୟଶ ൪ (4.3)
ˆ୧ ሺሻ ˆ୧ ሺͲሻ
ˆୢ ሺሻ ˆୢ ሺͲሻ

‫ۓ‬က‫ঁ؂‬᎖ᚆηࢂցёаԋфᙯඤࣁႝ৒೛ࣁᡂኧǴ ୩ (n)ࣁಃ k ঁ᎖ᚆη࿶ၸ n

଼ + 2Li → ‹ଶ ଼

‹ଶ ଼+2Li →‹ଶ ୬ +‹ଶ ଼ି୬

2‹ଶ ୬ +(2n-4)Li→n ‹ଶ ଶ (4.4)

‹ଶ ୬ +(2n-2)Li →n‹ଶ 

‹ଶ ଶ+2Li→2‹ଶ 

ԛ‫ޑ‬к‫ܫ‬ႝൻᕉࡕ٩ฅࣁࢲ៌‫ރ‬ᄊ‫ޑ‬යఈॶ(0<୩ <1)Ǵ ‫ځ‬ύ 1ʀ kʀmaxǴmax ࣁ

᎖౷ႝԣϣё֖Ԗ᎖ᚆηኧϐനεॶǶ࿶ၸ n ԛк‫ܫ‬ႝࡕࢂցࣁࢲ៌ёаஒԜ‫ۓ‬က

ࣁ၀᎖ᚆηࢂցԖୖᆶԄϐϸᔈǶཀջଶ੮ӧ‫ރ‬ᄊܵୟଵ ᆶܵୟଶ ‫ޑ‬ᐒ౗Ǵջˆୟଵ (n)+ ˆୟଶ (n)Ǵ

߾ˆୟଵ (n)+ ˆୟଶ (n)ё߄Ңࣁ аΠΟᜪձᐒ౗ϐуᕴ

୬
1. ଆ‫ۈ‬ਔӧୟଵ Ǵ࿶ၸ n ԛൻᕉࡕϝӧ ୟଵ ϐᐒ౗Ǵջࣁˆୟଵ ሺͲሻ ୟଵ՜ୟଵ
୬
2. ଆ‫ۈ‬ਔӧୟଶ Ǵ࿶ၸ n ԛൻᕉࡕϝӧ ୟଶ ϐᐒ౗Ǵջࣁˆୟଶ ሺͲሻୟଶ՜ୟଶ

30
3. ଆ‫ۈ‬ਔӧ୧ Ǵ࿶ၸ n ԛൻᕉࡕ‫ډ‬ၲ ୟଵ Ъ੮ӧୟଵ ϐᐒ౗Ǵջࣁ

୬ ୤౗భ ሺ଴ሻ୔౗భ՜ౚ
݂௜ ሺͲሻ୧՜ୟଵ = (ሺୟଵ՜ୟଵ ሻ୬ - ሺ୧՜୧ ሻ୬ ) (4.5)
୔౩՜౗భ ି୔౗భ՜ౚ

ࡺёளрԄ
୬ ୬ ୬
୩ ሺ݊ሻ = ˆୟଵ (n) + ˆୟଶ ሺሻ = ˆୟଵ ሺͲሻୟଵ՜ୟଵ +ˆୟଶ ሺͲሻୟଶ՜ୟଶ +ˆ୧ ሺͲሻ୧՜ୟଵ

୬ ୬ ୤౗భ ሺ଴ሻ୔౗భ՜ౚ
=ˆୟଵ ሺͲሻୟଵ՜ୟଵ + ˆୟଶ ሺͲሻୟଶ՜ୟଶ + (ሺͳ െ ୟଵ՜ୢ ሻ୬ -ሺͳ െ ୧՜ୟଵ ሻ୬ ) (4.6)
୔౩՜౗భ ି୔౗భ՜ౚ

٠‫ۓ‬ကୗ୷ୱ୲ୣ୫ ሺ݊ሻࣁ࿶ၸ n ԛк‫ܫ‬ႝࡕҞ߻‫ޑ‬ႝԣᕴႝ৒ໆ߾ǴЪଷ೛ଵ , ଶ ,…,

୫ୟ୶ ࣁᐱҥЪٰԾ‫࣬ܭ‬ӕϐ҆ᡏǴ߾

ୗ୷ୱ୲ୣ୫ ሺሻ =ଵ ሺሻ+ଶ ሺሻ+ଷ ሺሻ+…+୫ୟ୶ ሺሻ

= max(ˆ୬ୟଵ + ˆ୬ୟଶ )
୤బ౗భ ୔౗భ՜ౚ
= max[ˆ଴ୟଵ ሺୟଵ՜ୟଵ ሻ୬ +ˆ଴ୟଶ ሺܲ௔ଶ՜௔ଶ ሻ୬ + (ሺͳ െ ୟଵ՜ୢ ሻ୬ -ሺͳ െ ୧՜ୟ୧ ሻ୬ )]
୔౩՜౗భ ି୔౗భ՜ౚ

(4.7)

4.3 ႝ৒ໆѳ֡ϐόዴ‫܄ۓ‬
җ‫ܭ‬ଭёϻၸำ‫ڀ‬Ԗόዴ‫܄ۓ‬Ǵట௢ᆉр‫؂‬΋ԛк‫ܫ‬ႝࡕ‫ޑ‬όዴ‫܄ۓ‬ᡂϯǴሡ

ा‫ޕ‬ၰ‫؂‬ԛк‫ܫ‬ႝࡕ‫ޑ‬ሾୗ୷ୱ୲ୣ୫ ሺሻ]аϷƒ”ሾୗ୷ୱ୲ୣ୫ ሺሻ]Ƕ‫ۓ‬က x=a1 аϷ x=a2 ࣁԋ

фᙯඤࣁႝ৒ǴЪ x=i аϷ x=d ࣁѨ௳ᙯඤࣁႝ৒Ǵ߾ᡂኧ x ಄ӝқոΚϩଛǴᔈ

Ҕύѧཱུज़‫ۓ‬౛ཷ‫ۺ‬Ǵ྽ൻᕉԛኧ n ‫ۓڰ‬ਔǴଷ೛ᡂኧଵ , ଶ , ଷ ,…,୫ୟ୶ ֡ࣁϕ࣬

ᐱҥǴ߾ୗ୷ୱ୲ୣ୫ ሺሻ= ଵ + ଶ +ଷ +…+୫ୟ୶ ЪӢ max>>30ǴӢԜᡂኧୗ୷ୱ୲ୣ୫ ሺሻ཮ᖿ

߈‫ܭ‬தᄊϩթǶ

ሾୗ୷ୱ୲ୣ୫ ሺሻ]=maxሾˆ୬ୟଵ  ൅ ˆ୬ୟଶ ] (4.8)

ƒ”ሾୗ୷ୱ୲ୣ୫ ሺሻ]=max[ˆ୬ୟଵ + ˆ୬ୟଶ ][1- (ˆ୬ୟଵ +ˆ୬ୟଶ )] (4.9)

31
ಃϖകǵӚᜪձ᎖౷ႝԣ੝‫܄‬௖૸

Ԝക࿯ஒඔॊӚᅿόӕ‫ނཱུ҅ޑ‬፦ǴӧҁፕЎ‫ࡌ܌‬ҥϐ಍΋ࢎᄬΠǴаଭёϻ

ኳٰࠠඔॊ‫ޑ‬૰ଏ‫܄‬፦ǶԜኳࠠύ‫ୖޑ‬ኧёаೱ่‫ډ‬ς‫ނޑޕ‬౛ϯᏢ૰ଏၸำǴа

Ϸ‫ނ‬፦‫܄ޑ‬፦ǴࡺԜകҞ‫ޑ‬ӧ‫ܭ‬ග‫ٮ‬΋ঁёаග‫ٮ‬Ӛᜪձႝԣ੝‫ޑ܄‬ໆϯπ‫ڀ‬Ǵຑ

՗Ӛᅿόӕ‫ޑ‬೛ी‫נ‬᏷Ƕ

5.1 ଭёϻኳࠠୖኧኳᔕ
ӧԜଭёϻኳࠠϐύǴӅԖϤঁЬाᡂኧх֖Ǻ܎‫܉‬૚ ሺ૙ሻ, ܎‫܉‬૛ ሺ૙ሻ, ܎‫ ܌‬ሺ૙ሻ,‫܉۾‬૚՜‫ ܌‬,

‫܉۾‬૛՜‫ ܌‬, ‫ܑ۾‬՜‫܉‬૚ Ǵ‫ځ‬ᎩᡂኧࣣёᙖҗԜϤᡂኧ௢ॹԶளǶୖྣӚጇЎ᝘[32,33,34]ჴᡍ

ኧᏵǴ೛‫ ࣁࡋྕۓ‬25ƱC Ъႝࢬໆᓎ౗ࣁ 0.5C ϐΠǴ‫ڗ‬ள‫ځ‬к‫ܫ‬ႝԛኧ n=1 Կ

n=300 ႣෳኧᏵ‫ࢂ܈‬ჴᡍኧᏵǴᙖҗ಍ी೬ᡏ SPSS ୖኧኳᔕ߾ёаளраΠϐኳ

ᔕኧᏵǴᙖԜٰඔॊӚঁ᎖౷ႝԣӧԜଭёϻኳࠠϐύǶԜኳᔕБ‫܌ݤ‬ளϐୖኧᆶ

Sebastian Risse ‫ ܭ‬2015 ԃගр‫[زࣴޑ‬31]Μϩ࣬՟ǴӢԜҁፕЎ‫܌‬٬Ҕϐୖኧ

܎‫܉‬૚ ሺ૙ሻ, ܎‫܉‬૛ ሺ૙ሻ, ܎‫ ܌‬ሺ૙ሻ,‫܉۾‬૚՜‫ ܌‬, ‫܉۾‬૛՜‫ ܌‬, ‫ܑ۾‬՜‫܉‬૚ ୖ᎙Ў᝘ϐኧᏵமϯኳᔕ‫ޑ‬ᆒྗࡋǴӚ

ᜪձ᎖౷ႝԣϐୖኧӵ߄ 2Ƕ

߄ 2 Ӛᜪձ᎖౷ႝԣୖኧКၨ

Battery
܎‫܉‬૚ ሺ૙ሻ ܎‫܉‬૛ ሺ૙ሻ ܎࢏ ሺ૙ሻ ܎‫ ܌‬ሺ૙ሻ ‫܉۾‬૚՜‫ ܌‬ሾ૚૙ି૜ ሿ ‫܉۾‬૛՜‫ ܌‬ሾ૚૙ି૜ ሿ ‫ܑ۾‬՜‫܉‬૚ ሾ૚૙ି૜ ሿ
Category

΋૓(LS) 0.42 0.20 0 0.38 2.61 35.6 0

ҡᏀମࢎ(Co) 0.57 0.11 0 0.32 1.01 60.0 0

਼ϯ⑲(‹ଶ ) 0.48 0 0.02 0.50 2.70 0 553

ᙻ୷݈(Ni) 0.33 0.49 0.18 0 1.18 733 312

ຏ 1Ǻ܎‫܉‬૚ ሺ૙ሻΠ‫ޑ‬Ѥಔኧӷϩձ߄ҢѤᅿᜪձႝԣ‫ܭ‬ᛙ
ᛙ‫ރ៌ࢲޑۓ‬ᄊ‫܉܁‬૚ ߃‫ۈ‬ᐒ౗Ƕ
32
ӕ౛ ܎‫܉‬૛ ሺ૙ሻǡ ܎࢏ ሺ૙ሻǡ ܎‫ ܌‬ሺ૙ሻ߾߄ҢӚԾ‫ރ‬ᄊΠѤᅿᜪձႝԣЍ߃‫ۈ‬ᐒ౗Ƕ

ຏ 2Ǻ‫܉۾‬૚՜‫ ܌‬ሾ૚૙ି૜ ሿ Π‫ޑ‬Ѥಔኧӷϩձ߄ҢѤᅿᜪձႝԣҗᛙ

ᛙ‫ރ៌ࢲޑۓ‬ᄊ‫܉܁‬૚ᙯ౽

ԝΫ‫ރ‬ᄊ‫ޑ ܌܁‬ᙯ౽ᐒ౗Ƕӕ౛ ‫܉۾‬૛՜‫ ܌‬ሾ૚૙ି૜ ሿǡ ‫ܑ۾‬՜‫܉‬૚ ሾ૚૙ି૜ ሿ ҭ߄Ңόӕ‫ރ‬ᄊ໔‫ޑ‬ᙯ

Կԝ

౽ᐒ౗Ƕ

5.2 ႝԣႝ৒ໆΠफ़Ԕጕᆶᡂ౦ኧϩ‫݋‬
࿶җ C# ኗቪำԄ(ำԄዸёୖྣߕᒵ 1)Ǵаંତ࣬४БԄीᆉрଭёϻᙯ౽ᐒ
୬ ୬ ୬
౗Ǵ߾ёаள‫ډ‬ୟଵ՜ୟଵ ǡ ୟଶ՜ୟଶ ǡ ୧՜ୟଵ ฻ᙯ౽ᐒ౗Ǵ࿶җԄ 4.7 ёаीᆉрୗ୷ୱ୲ୣ୫ ሺሻǴ

ջࣁ᎖౷ႝԣӧόӕк‫ܫ‬ႝԛኧ n Π‫܌‬ഭᎩϐႝ৒ໆǴკ 8 ࣁѤᅿ᎖౷ႝԣ࿶җଭ

ёϻၸำीᆉࡕႝ৒ໆ‫ޑ‬Πफ़ԔጕǶӧ 5.2 ύ‫཮ॺך‬ឍॊόӕᜪձ᎖౷ႝԣႝ৒ໆ

Πफ़ԔጕаϷᆶୖኧ‫܌‬ж߄ϐཀ఼Ƕ

კ 8 Ӛᜪձ᎖౷ႝ৒ໆΠफ़ԔጕКၨ

5.2.1 ᎖౷ႝԣ(LS)к‫ܫ‬ႝϐ૰ଏԔጕ

୷‫ ߄ܭ‬3 ϐୖኧǴკ 9 Ѱკࣁ࿶җำԄኳᔕ‫܌‬ள‫ޑډ‬ႝ৒ໆΠफ़ԔጕǴკ 9 ѓ

კࣁচ‫ۈ‬Ў᝘ჴᡍ‫܌‬ள‫ޕ‬ႝ৒ໆΠफ़ኧᏵ[32]Ǵᙖҗკ 9 Кၨёள‫ޕ‬ኳᔕрୖኧ‫܌‬

ᇙႝ৒ໆΠफ़Ԕጕᆶচ‫ۈ‬ჴᡍኧᏵ‫܌‬ளႝ৒ໆΠफ़Ԕጕ࣬՟ࡋߚதଯǹკ 12 ࣁк

‫ܫ‬ႝԛኧ n ᆶႝԣᡂ౦ჹᔈ‫ޑ‬ԔጕǶ

௖૸‫ځ‬૰ଏԔጕ‫ޑ‬Πफ़௃‫׎‬Ǵ᎖౷ႝԣ(LS)‫ځ‬૰ଏೲࡋܴᡉၨ‫ځ‬Ѭᜪձႝԣ‫׳‬

33
у‫ז‬ೲǴচӢࣁǴ᎖౷ႝԣ(LS)ཱུ҅ࣁ 100%౷ǴԶ౷‫ޑ‬ᚆηᏤႝ‫ک܄‬ႝηᏤႝ‫܄‬೿

ࡐեǴᏤठႝཱུύ౷‫ޑ‬ႝϯᏢ‫ૈ܄‬ό٫ϷճҔ౗եǴӧൻᕉၸำύ᎖౷ႝԣ(LS)ύ

౷ႝཱུ‫ޑ‬ᡏᑈ‫׎‬ᡂଯၲ 22%ёૈ٬౷ႝཱུϣ೽ౢғ༾຋દᇿ೭ᅿ༾຋દ‫ޑ‬ӸӧϷ㶥

ጔ࣬‹ଶ ӧ຋દೀ‫ޑ‬ғԋઇᚯΑႝཱུ‫ޑ‬᏾ᡏ‫܄‬Ǵനಖуቃ᎖౷ႝԣ‫ޑ‬৒ໆ૰ଏӢԜ

όፕࢂୟଵ՜ୢ ‫ ࢂ܈‬ୟଶ՜ୢ ӧѤᅿႝԣϐύ೿ୃଯǶ

߄ 3 ᎖౷ႝԣ(LS)ଭёϻၸำୖኧ

Battery
܎‫܉‬૚ ሺ૙ሻ ܎‫܉‬૛ ሺ૙ሻ ܎࢏ ሺ૙ሻ ܎‫ ܌‬ሺ૙ሻ ‫܉۾‬૚՜‫ ܌‬ሾ૚૙ି૜ ሿ ‫܉۾‬૛՜‫܌‬ሾ૚૙ି૜ ሿ ‫ܑ۾‬՜‫܉‬૚ ሾ૚૙ି૜ ሿ
Category

LS 0.42 0.20 0 0.38 2.61 35.6 0

კ 9 ᎖౷ႝԣ(LS)ႝ৒ໆኳᔕΠफ़ԔጕᆶჴᡍΠफ़Ԕጕ

34
 კ 10 ᎖౷ႝԣ(LS)ᡂ౦ኧᆶ೯‫ܫ‬ႝԛኧᜢ߯

5.2.2 ҡᏀମࢎ-᎖౷ႝԣ(Co)к‫ܫ‬ႝϐ૰ଏԔጕ

୷‫ ߄ܭ‬4 ϐୖኧǴკ 11 ࣁ࿶җำԄኳᔕ‫܌‬ள‫ډ‬к‫ܫ‬ႝԛኧ n ᆶ৒ໆჹᔈ‫ޑ‬Π

फ़Ԕጕǹკ 12 ࣁк‫ܫ‬ႝԛኧ n ᆶႝԣᡂ౦ჹᔈ‫ޑ‬ԔጕǶҗკ 10 ёள‫ޕ‬ᙖҗӧཱུ҅

ቚуҡᏀମࢎᡣ౷Ԗਏ‫ۓڰ‬ԋфफ़եόᛙ‫ۓ‬ୟଶ ‫ރ‬ᄊ߃‫ۈ‬ᐒ౗Ǵཀջˆୟଶ ሺͲሻε൯‫ޑ‬Π

फ़Ƕ

Sun[32]ࣴ‫ز‬ҡᏀମࢎჹ‫ܭ‬᎖౷ႝԣύ֖౷‫ཱུ҅ޑ‬к‫܄ܫ‬ϐቹៜǶӧჴᡍύǴ౷

ૈԋфॄၩࢂ೸ၸΒ౷ϯణӧύϾҡᏀମࢎ‫ޑ‬໽ϯ਼ϯϸᔈǴаϷᅙᑼ੆ᅄ‫ݤ‬ǶǶ

Ԝჴᡍ‫ׯޑ‬຾೽ϩԖ‫ٿ‬ᗺǴ२Ӄࢂкᅈේ‫ޑ‬ҡᏀମࢎǴӆٰࢂ໽ϯ਼ϯϸᔈǴΨ൩

ࢂૈᡣ౷চηᆶҡᏀମࢎᆙஏௗӝ‫ޑ‬΋ቫቫ౷؈ᑈǴ೭ᡣ౷ૈ୼Ԗਏ౗‫ۓڰޑ‬Ƕк

ᅈේ‫ޑ‬ҡᏀаϷ໽ϯ਼ϯϸᔈǴ೭‫ۺཷঁٿ‬ᡣк‫ܫ‬ਏ౗Ԗᡉ๱‫ޑ‬ගϲǶж߄ߏਔ໔

ൻᕉ‫ˆޑ܄‬ୟଵ ሺͲሻǴ‫ځ‬ໆԖ‫܌‬ቚуǴԶόᛙ‫ރ៌ࢲۓ‬ᄊ‫ˆޑ‬ୟଶ ሺͲሻࠅ෧ϿǴˆୟଶ ሺͲሻ‫ז‬ೲӦҗ

ࢲ‫ރ܄‬ᄊᙯඤԋഈԝ‫ރ‬ᄊǶќѦǴచҹ‫ޑ‬ᙯඤᐒ౗ୟଵ՜ୢǴ٬ᛙӦࢲ‫ރ܄‬ᄊ‫ޑ‬ਔ໔ቚ

ߏǶ٠ؒԖᢀჸ‫ރډ‬ᄊˆ୧ ሺͲሻౢғǶ

35
 ߄ 4 ᎖౷ႝԣ(CO)ଭёϻၸำୖኧ

Battery
܎‫܉‬૚ ሺ૙ሻ ܎‫܉‬૛ ሺ૙ሻ ܎࢏ ሺ૙ሻ ܎‫ ܌‬ሺ૙ሻ ‫܉۾‬૚՜‫ ܌‬ሾ૚૙ି૜ ሿ ‫܉۾‬૛՜‫ ܌‬ሾ૚૙ି૜ ሿ ‫ܑ۾‬՜‫܉‬૚ ሾ૚૙ି૜ ሿ
Category

CO 0.57 0.11 0 0.32 1.01 60.0 0

კ 11 ᎖౷ႝԣ(CO)ႝ৒ໆኳᔕΠफ़Ԕጕ

კ 12 ᎖౷ႝԣ(CO)ᡂ౦ኧᆶ೯‫ܫ‬ႝԛኧᜢ߯

36
5.2.3 Β਼ϯ⑲-᎖౷ႝԣ(‫۽ܑ܂‬૛ )к‫ܫ‬ႝϐ૰ଏԔጕ

୷‫ ߄ܭ‬5 ϐୖኧǴკ 13 Ѱკࣁ࿶җำԄኳᔕ‫܌‬ள‫ޑډ‬ႝ৒ໆΠफ़ԔጕǴკ 13

ѓკࣁচ‫ۈ‬Ў᝘ჴᡍ‫܌‬ள‫ޕ‬ႝ৒ໆΠफ़ኧᏵ[33] ǹკ 14 ࣁк‫ܫ‬ႝԛኧ n ᆶႝԣᡂ

౦Ƕჹᔈ‫ޑ‬Ԕጕᙖҗკ 9 Кၨёள‫ޕ‬ኳᔕрୖኧ‫܌‬ᇙႝ৒ໆΠफ़Ԕጕᆶচ‫ۈ‬ჴᡍኧ

Ᏽ‫܌‬ளႝ৒ໆΠफ़Ԕጕ࣬՟ࡋߚதଯǶҗკ 13 ёள‫ޕ‬ᙖҗӧཱུ҅ቚуΒ਼ϯ⑲ෘ

аೈ໳─ೈෘ‫ޑ‬БԄᡣ౷Ԗਏ‫ۓڰ‬ԋфफ़եόᛙ‫ۓ‬ୟଶ ‫ރ‬ᄊ߃‫ۈ‬ᐒ౗Ǵཀջˆୟଶ ሺͲሻε

൯‫ޑ‬Πफ़Ƕ

Ding[33]௦Ҕ࠾း‫ޑ‬౷‫ރ‬ᄊᆶΒ਼ϯ⑲Ƕӧࣴ‫ز‬ύஒ౷੆ᅄӧԖϾ‫ޑ‬Β਼ϯ⑲

่ᄬύǴ٠ᆶ΋૓‫ޑ‬ҡᏀπբႝཱུКၨǶǶΒ਼ϯ⑲‫ޑ‬٬ҔǴᡣ‫ॺך‬ᢀჸ‫ރ܄ࢲډ‬

ᄊ‫ۯ‬ᒨញрǴᏤठႝ৒ໆୗ୷ୱ୲ୣ୫ ሺሻӧ 0<n<11 ԛൻᕉύቚуǴаϷၨଯൻᕉԛኧᒿ

ϐ෧ϿǶӵӃ߻ှញ‫ޑ‬ǴԔጕ‫ރکރ׎ޑ‬ᄊˆ୧ р౜ԖᜢǶୖኧཀ‫ښ‬όᛙ‫ރ܄ࢲۓ‬ᄊ

ˆୟଶ ‫ޑ‬෧১ǴΨཀ‫ښ‬ᛙ‫ރ܄ࢲۓ‬ᄊˆୟଵ ‫ޑ‬ቚуǴࢂҗόࢲ៌‫ރ‬ᄊˆ୧ ‫ޑ‬р౜ՔᒿౢғǴӕ

ਔǴచҹᙯඤᐒ౗ୟଵ՜ୢ ෧ϿǶ೭మཱ‫߄ޑ‬Ң᎖ႝԣߏය‫ޑ‬ᛙ‫܄ۓ‬Ԗ‫܌‬຾‫؁‬ǶDing Ψ

߄ҢǴLixTiO2 ೱុ‫ޑ‬চՏғԋᔅշႝ಻ၩη e-/Li+‫ޑ‬ᏤႝǶ೭ঁᐒ‫୼ૈڋ‬ှញ߻൳

ԛൻᕉύ৒ໆԔጕ‫ޑ‬΢ϲǴΨӢԜж߄Ӄ߻ߚࢲ‫ރ܄‬ᄊ‫ࢲޑ‬ϯǶ

Β਼ϯ⑲ෘ‫ޑ‬٬ҔǴᡣᛙ‫ރ܄ࢲۓ‬ᄊˆୟଵ ӢΒ਼ϯ⑲Ƕᗨฅೈ໳─ೈෘБ‫ݤ‬ύˆୟଵ

‫ॶޑ‬КਡෘᗭаೈෘБԄхᙟనᄊ౷Զ΢ϲǴՠΨӢ೽ϩ‫ޜ‬໔‫ڙ‬Β਼ϯ⑲՞ᏵǴૈ

ᆶ᎖ᚆηϸᔈϐ౷ᚆηኧໆӢԶफ़եᏤठˆୢ ΢ϲǴӆ‫ޣ‬Ƕ྽่඲‫׎‬౷ᙯᡂԋ౷ϯ᎖

ٰ‫ډ‬ऊԭϩϐΖΜ‫ޑ‬ำࡋਔǴ৒ໆε൯‫ޑ‬ᘉ஭ǴଞჹԜ౜ຝǴ‫܌‬ᔈҔ‫ࢂޑ‬ೈ໳─ೈෘ

Б‫ݤ‬Ƕऩ۹ຎΑᑩ๞‫ޑ‬ၸำǴΒ਼ϯ⑲‫ޑ‬ෘёૈ཮Ӣࣁ֖౷‫ޑ‬ਡЈᗭಈԶ຋໒Ƕ

37
 ߄ 5 ᎖౷ႝԣ(‹ଶ )ଭёϻၸำୖኧ

Battery
܎‫܉‬૚ ሺ૙ሻ ܎‫܉‬૛ ሺ૙ሻ ܎࢏ ሺ૙ሻ ܎‫ ܌‬ሺ૙ሻ ‫܉۾‬૚՜‫ ܌‬ሾ૚૙ି૜ ሿ ‫܉۾‬૛՜‫ ܌‬ሾ૚૙ି૜ ሿ ‫ܑ۾‬՜‫܉‬૚ ሾ૚૙ି૜ ሿ
Category

‹ଶ 0.48 0 0.02 0.50 2.70 0 553

კ 13 ᎖౷ႝ(‹ଶ ሻႝ৒ໆኳᔕΠफ़ԔጕᆶჴᡍΠफ़Ԕጕ

კ 14 ᎖౷ႝԣ(‹ଶ )ᡂ౦ኧᆶ೯‫ܫ‬ႝԛኧᜢ߯

38
5.2.4 ᙻ୷݈-᎖౷ႝԣ(Ni)к‫ܫ‬ႝϐ૰ଏԔጕ

୷‫ ߄ܭ‬6 ϐୖኧǴკ 15 ࣁ࿶җำԄኳᔕ‫܌‬ள‫ډ‬к‫ܫ‬ႝԛኧ n ᆶ৒ໆჹᔈ‫ޑ‬Π

फ़ԔጕǴკ 16 ࣁк‫ܫ‬ႝԛኧ n ᆶႝԣᡂ౦ჹᔈ‫ޑ‬ԔጕǶҗკ 10 ёள‫ޕ‬ᙖҗӧཱུ҅

ቚу௦ҔԖϾ‫݈୷ᙻݣݰޑ‬ᗨฅ٠҂फ़եόᛙ‫ۓ‬ୟଶ ‫ރ‬ᄊ߃‫ۈ‬ᐒ౗Ǵՠԋфफ़եୢ ԝ

Ϋ‫ރ‬ᄊ߃‫ۈ‬ᐒ౗Ǵ٠ගଯ୧ ߚࢲ៌‫ރ‬ᄊ‫ۈ߃ޑ‬ᐒ౗ǴӢԜკ 10 ύǴ‫ ܭ‬n<25 ਔёа

ܴᡉ‫࣮ޑ‬рୗ୷ୱ୲ୣ୫ ሺሻႝ৒ໆӣϲǶ

Chung and Manthiram[34]௦ҔԖϾ‫݈୷ᙻݣݰޑ‬ǴϾ৩εཷӧ 100 mm ѰѓǴа

ၲ‫ډ‬ᚈ‫ ૈ۔‬3D ౷ᙻ‫ཱུ҅ݣݰ‬Ƕ೭٤੝ձ‫ނཱུ҅ޑ‬፦ჹԖ๱ߎឦ߄य़‫ޑ‬౷ᏱԖࡐம

‫ޑ‬ϯᏢ֎ԏ‫܄‬ǴӢԜૈ୼ԋфज़‫ڋ‬ႝηϣ೽‫ޑ‬ӭ౷ϯ‫ނ‬ǶќѦǴ‫ᙻݣݰ‬Ψ଺ࣁࡐ෇

‫ޑ‬ϣ೽ႝη໺ሀᆛ๎Ƕ

60%ᐚࡋ౷֖ໆ‫ཱུ҅ޑ‬Ǵᡉ౜΋૓ҡᏀཱུ҅‫ޑࠠڂ‬৒ໆ૰ଏǴ཮Ӄ‫ז‬ೲΠफ़Ȑό

ᛙ‫ރ܄ࢲۓ‬ᄊ‫܉܁‬૛ ȑǴௗ๱጗ᄌ૰ଏȐᛙ‫ރ܄ࢲۓ‬ᄊ‫܉܁‬૚ ȑǴҗ‫܌ᙻݣݰ‬ᇙ‫ཱུ҅ޑ‬Ǵ‫ঁٿ‬

Ԕጕ೿Ԗᅵ઀‫ރ‬ᄊр౜Ƕᛙ‫ރ܄ࢲۓ‬ᄊᆶᅵ઀‫ރ‬ᄊ‫ޑ‬ᕴ‫ک‬Ȑfliv1+fsȑவ 0.38 ቚуԿ

0.44 а΢ǴനࡕԿ 0.51Ǵཱུ҅ϩձࢂ΋૓ཱུ҅ǵߎឦʏ౷Ȑ60 ԭϩᐚࡋȑཱུ҅Ǵߎ

ឦʏ౷Ȑ70 ԭϩᐚࡋȑཱུ҅Ƕkliv1→d ୖኧ‫ׯॶޑ‬ᡂள‫ࣁ׳‬ᡉ๱Ǵж߄ߏය‫ޑ‬ᛙ‫ۓ‬

‫܄‬Ƕ

߄ 6 ᎖౷ႝԣ(Ni)ଭёϻၸำୖኧ

Battery
܎‫܉‬૚ ሺ૙ሻ ܎‫܉‬૛ ሺ૙ሻ ܎࢏ ሺ૙ሻ ܎‫ ܌‬ሺ૙ሻ ‫܉۾‬૚՜‫ ܌‬ሾ૚૙ି૜ ሿ ‫܉۾‬૛՜‫ ܌‬ሾ૚૙ି૜ ሿ ‫ܑ۾‬՜‫܉‬૚ ሾ૚૙ି૜ ሿ
Category

Ni 0.33 0.49 0.18 0 1.18 733 312

39
 კ 15 ᎖౷ႝԣ(Ni)ႝ৒ໆኳᔕΠफ़Ԕጕ

კ 16 ᎖౷ႝԣ(Ni)ᡂ౦ኧᆶ೯‫ܫ‬ႝԛኧᜢ߯

40
ಃϤകǵӚᜪձ᎖౷ႝԣё᎞ࡋϩ‫݋‬

ҁക࿯ᙖҗಃϖകଭёϻኳࠠ‫܌‬ள‫ޑډ‬᎖౷ႝԣႝ৒ໆǵᡂ౦ኧᆶк‫ܫ‬ႝԛኧ

(n)ϐ໔‫ޑ‬ᜢ߯Ǵ‫ۯ‬՜௖૸྽к‫ܫ‬ႝԛኧ(n)‫ۓڰ‬ᆶ‫ۓ‬ကѨਏำࡋΠǴӚᜪձႝԣ‫ޑ‬ё

᎞ࡋᡂϯǴٰຑ՗Ӛᅿόӕ‫׷ޑ‬፦‫נ‬᏷ᆶόӕѨਏำࡋ‫ۓ‬က໔ᜢ߯ࢂӵՖቹៜႝԣ

ё᎞ࡋǶ6.1 ࿯ϟಏӵՖӧԜࣴ‫ز‬ϐύǴӵՖ‫ۓ‬ကё᎞ࡋǴаϷ‫ځ‬ीᆉБԄǹ6.2 ࿯

Կ 6.4 ࿯௖૸ӧ‫ۓڰ‬όӕѨਏᖏࣚॶΠӚᜪձ᎖౷ႝԣё᎞ࡋᡂϯǹ6.5 ࿯௖૸ӧ࣬

ӕ᎖౷ႝԣύǴόӕѨਏᖏࣚॶΠё᎞ࡋᡂϯǶ

6.1 ཷ‫ۺ‬ϟಏᆶё᎞ࡋ‫ۓ‬က
State Of Health(SOH) ႝԣ଼ந‫ރ‬ᄊࡰ‫ࢂޑ‬ᆶӄཥႝԣ࣬КၨΠǴ‫ځ‬੝‫ۓ‬ϐ‫ૈ܄‬

‫ރ‬ᄊ‫ޑ‬ໆෳྗ߾Ǵӧк‫ܫ‬ႝԛኧ(n)‫ۓڰ‬ΠਥᏵԄ 2.2 ёள
େ౩౯౩౪౛ౣ ሺ୬ሻ
SOH(n)= େౣ౗౮
× 100% (6.1)

‫ځ‬ύୱ୷ୱ୲ୣ୫ ሺሻܺவதᄊϩթǴ୫ୟ୶ ࣁ‫ۓڰ‬தኧǴதᄊᡂኧᆶதኧϐ४ନࣁ‫ރ׎‬ᡂϯǴ

ଵ଴଴Ψ
߾Ӣࣁ SOH(n)=ୱ୷ୱ୲ୣ୫ ሺሻ × େ Ǵࡺ SOH(n)ҭܺவதᄊϩթǶ‫ۓ‬က Q ࣁႝԣѨਏ
ౣ౗౮

ᖏࣚॶϐᒿᐒᡂኧǴ߾ӧ n ‫ۓڰ‬Π‫س‬಍ё᎞ࡋёаҗаΠԄη߄Ң

 ୱ୷ୱ୲ୣ୫ (n)=Pr[Q< ሺሻሿ

ஶ ୗ୓ୌሺ୬ሻ
=‫׬‬଴ ሾ‫׬‬଴ ˆ୕ ሺ“ሻ†“ሿˆௌைுሺ௡ሻ ሾ ሺሻሿ† ሺሻ  (6.2)

ୗ୓ୌሺ୬ሻ
=‫׬‬଴ ˆ୯ ሾ ሺሻሿˆୗ୓ୌሺ୬ሻ ሾ ሺሻሿ† ሺሻ

ӧҁፕЎύǴԵቾᇙ೷୘཮ஒ Q ‫ۓ‬ကࣁ΋‫ۓڰ‬ኧॶǴதኧ qǴБߡ‫ڰߥۓڋ‬฼

ౣǴӆ‫ޣ‬Ӣ ሺሻܺவதᄊϩଛǴࡺ

୯ିஜሺ୬ሻ
 ୱ୷ୱ୲ୣ୫ (n) = Pr[q< ሺሻሿ = Pr[ < ሿ (6.3)
஢ሺ୬ሻ

‫ځ‬ύǴɊሺሻࣁ ሺሻϐයఈॶЪɐሺሻࣁ ሺሻ኱ྗৡǴ ୱ୷ୱ୲ୣ୫ (n)ёҗკ 17 ߄ҢǶ

41
 კ 17 к‫ܫ‬ႝԛኧ(n)‫ۓڰ‬Πё᎞ࡋ

٩Ԅ 6.3 ёஒӚᜪձ᎖౷ႝԣीᆉр n=1 Կ n=300 ϐё᎞ࡋǴ٠ᇙբрё᎞ࡋ

ԔጕǴკ 17 (a)а Ni ᎖౷ႝԣࣁ‫ٯ‬Ǵᇙբр n=1 Կ n=300 ϐ ୱ୷ୱ୲ୣ୫ Πफ़ԔጕǴ೛

q=80%Ǵ྽ൻᕉԛኧ n=150 ਔǴ ୱ୷ୱ୲ୣ୫ (150)ёҗკ 17 (b)ϐதᄊϩଛीᆉளр

P[ ୱ୷ୱ୲ୣ୫ (150) > 0.8] =0.885

კ 18 ᎖౷ႝԣ(Ni)‫س‬಍ё᎞ࡋҢཀკ

42
6.2 ‫ۓ‬ကႝԣ଼ந‫ݩރ‬ե‫ ܭ‬80%ࣁѨਏΠё᎞ࡋϩ‫݋‬
ҁ࿯೛‫ۓ‬ႝԣ଼ந‫ ݩރ‬SOH ե‫ ܭ‬80%ਔࣁѨਏǴ೛ q ࣁѨਏᖏࣚॶǴ྽к‫ܫ‬

ႝԛኧ(n)‫ۓڰ‬ਔǴq=80%ਔ߾ёฝр‫س‬಍ё᎞ࡋ ୱ୷ୱ୲ୣ୫ (n) = Pr[80%< ሺሻሿჹᔈ

‫ޑ‬ᗺǴ٠Ъीᆉ n=1 Կ n=300 ਔ‫سޑ‬಍ё᎞ࡋ ୱ୷ୱ୲ୣ୫ (n)Ǵ߾ёᛤᇙ࣬ჹ‫ޑ‬ё᎞ࡋԔ

ጕǴკ 19 ࣁѤᅿᜪձႝԣ‫܌‬ᇙ q=80%ਔӚᜪձ᎖౷ႝԣ ୱ୷ୱ୲ୣ୫ Πफ़ԔጕǶᒿࡕ 6.2.1

λ࿯Կ 6.2.4 λ࿯ϩձϟಏӚᜪձ᎖౷ႝԣ ୱ୷ୱ୲ୣ୫ Πफ़ԔጕǴ٠Ъа SigmaPlot 12.0

ϩଛኳᔕଛჹрӚԔጕനӝ፾ϐё᎞ࡋ ୱ୷ୱ୲ୣ୫ ‫ڄ‬ኧǴБߡᇙ೷୘ᆶ٬Ҕ‫ז׳ޣ‬ೲᆶ

ᆒዴ‫פޑ‬рჹᔈё᎞ࡋǶ

კ 19 q=80%ࣁѨਏΠё᎞ࡋԔጕ

43
6.2.1 ᎖౷ႝԣ(LS)ё᎞ࡋϩ‫݋‬

ӧа q=80% നࣁѨਏำࡋਔǴҗीᆉ่݀ᆶკ 19 ࣣёள‫ޕ‬྽᎖౷ႝԣ(LS) n=0

Կ n=11 ਔё᎞ࡋࣣᖿ߈‫ ܭ‬1 (Ѥ௭ϖΕԿλኧᗺΠಃѤՏ)Ǵ٠Ъ྽ n ε‫ܭ‬฻‫ ܭ‬42

ࡕ‫ځ‬ё᎞ࡋஒᖿ߈‫ ܭ‬1ǴӢԜаኳᔕ೬ᡏ SigmaPlot ଞჹ 11<n<42 ೽ϩԔጕ଺рന

٫‫ڄ‬ኧኳᔕǶ‫܌‬ኳᔕр LS ᎖౷ႝԣϐ‫س‬಍ё᎞ ୐ୗǡୱ୷ୱ୲ୣ୫ (n)ኳᔕрϐБำԄ‫ ځ‬Rɼ

1, ଶ ɼ1 (Ѥ௭ϖΕԿλኧᗺΠಃѤՏ)

ؒ1, 0‫أ‬n‫أ‬11ġ

଴Ǥଽଶଵ଼ି଴Ǥଵଵ଻଻୬ା଴Ǥ଴଴଺୬మ ି଴Ǥ଴଴଴ଵ୬య ା൫ଵǤ଼ସ଼ଶൈଵ଴షల ൯୬ర

 ୐ୗǡୱ୷ୱ୲ୣ୫ (n)ġ = , 11<n<42 ġ
ଵି଴Ǥଵସଵ଻୬ା଴Ǥ଴଴ଽଵ୬మ ି଴Ǥ଴଴଴ସ୬య ାሺଽǤ଴ଷଷଷൈଵ଴షల ሻ୬ర

ؒ0, n‫ؤ‬42 (6.4)

კ 20 ᎖౷ႝԣ(LS) 11<n<42 Ԕጕኳᔕ

44
6.2.2 ᎖౷ႝԣ(CO)ё᎞ࡋϩ‫݋‬

ӧа q=80% നࣁѨਏำࡋਔǴҗीᆉ่݀ᆶკ 19 ࣣёள‫ޕ‬྽᎖౷ႝԣ(CO)

n=0 Կ n=17 ਔё᎞ࡋࣣᖿ߈‫ ܭ‬1 (Ѥ௭ϖΕԿλኧᗺΠಃѤՏ)Ǵ٠Ъ྽ n ε‫ܭ‬฻‫ܭ‬

251 ࡕ‫ځ‬ё᎞ࡋஒᖿ߈‫ ܭ‬1ǴӢԜаኳᔕ೬ᡏ SigmaPlot ଞჹ 17<n<251 ೽ϩԔጕ଺

рന٫‫ڄ‬ኧኳᔕǶӧа q=80% നࣁѨਏำࡋਔǴ‫܌‬ኳᔕр CO ᎖౷ႝԣϐ‫س‬಍ё᎞

ࡋ େ୓ǡୱ୷ୱ୲ୣ୫ (n)ኳᔕрϐБำԄ‫ ځ‬Rɼ1, ଶ ɼ1(Ѥ௭ϖΕԿλኧᗺΠಃѤՏ)Ƕ

ؒ 1
1,
ġ 0‫أ‬n‫أ‬17ġ
 େ୓ǡୱ୷ୱ୲ୣ୫ (n)ġ ଴Ǥ଼ଽଶ଻ି଴Ǥ଴ଶ଴ଵ୬ା଴Ǥ଴଴଴ଶ୬మ ିሺ଺Ǥ଴ହଵସൈଵ଴షళ ሻ୬య
=ġ , 17<n<251 ġ
ଵି଴Ǥ଴ଶଽ଻୬ା଴Ǥ଴଴଴ଽସିሺଶǤ଻଻ଶ଻ൈଵ଴షల ሻ୬య ାሺଵǤଷ଺ହଵൈଵ଴షఴ ሻ୬ర

ؒ ġ0
0, n‫ؤ‬251ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ ġ (6.5)

კ 21 ᎖౷ႝԣ(CO) 17<n<251 Ԕጕኳᔕ

45
 6.2.3 ᎖౷ႝԣ(‫۽ܑ܂‬૛ )ё᎞ࡋϩ‫݋‬

ӧа q=80% നࣁѨਏำࡋਔǴҗीᆉ่݀ᆶკ 19 ࣣёள‫ޕ‬྽᎖౷ႝԣ(CO)

n=0 Կ n=38 ਔё᎞ࡋࣣᖿ߈‫ ܭ‬1 (Ѥ௭ϖΕԿλኧᗺΠಃѤՏ)Ǵ٠Ъ྽ n ε‫ܭ‬฻‫ܭ‬

181 ࡕ‫ځ‬ё᎞ࡋஒᖿ߈‫ ܭ‬1ǴӢԜаኳᔕ೬ᡏ SigmaPlot ଞჹ 38<n<181 ೽ϩԔጕ଺

рന٫‫ڄ‬ኧኳᔕǶӧ q=80% നࣁѨਏำࡋਔǴ‫܌‬ኳᔕр‹ଶ ᎖౷ႝԣϐ‫س‬಍ё᎞

 ୘୧୓మ ǡୱ୷ୱ୲ୣ୫ (n)ኳᔕрϐБำԄ‫ ځ‬R ɼ 0.9999, ଶ ɼ0.9997(Ѥ௭ϖΕԿλኧᗺΠಃ

ѤՏ)Ƕ

ؒ 1, 0‫أ‬n‫أ‬38ġ

 ୘୧୓మ ǡୱ୷ୱ୲ୣ୫ (n)ġ = ଴Ǥଷ଴଻ସି଴Ǥ଴଴଺ଵ୬ା൫ସǤ଴ଷ଻ଶൈଵ଴షఱ ൯୬మ ିሺ଼Ǥଽ଴଺଺ൈଵ଴షఴ ሻ୬య

, 38<n<181 ġ
ଵି଴Ǥ଴ସ଺ଷ୬ା଴Ǥ଴଴଴ଽ୬మ ିሺ଼Ǥସ଴ଷଽൈଵ଴షల ሻ୬య ାሺଶǤଽଽଽ଼ൈଵ଴షఴ ሻ୬ర

ؒ 0, n‫ؤ‬181
ؒ (6.6)ġ

კ 22 ᎖౷ႝԣ(‹ଶ ) 38<n<181 Ԕጕኳᔕ

46
 6.2.4 ᎖౷ႝԣ(‫)ܑۼ‬ё᎞ࡋϩ‫݋‬

ӧа q=80% നࣁѨਏำࡋਔǴҗीᆉ่݀ᆶკ 19 ࣣёள‫ޕ‬྽᎖౷ႝԣ(CO)

n=0 Կ n=65 ਔё᎞ࡋࣣᖿ߈‫ ܭ‬1 (Ѥ௭ϖΕԿλኧᗺΠಃѤՏ)Ǵ٠Ъ྽ n ε‫ܭ‬฻‫ܭ‬

301 ࡕ‫ځ‬ё᎞ࡋஒᖿ߈‫ ܭ‬1ǴӢԜаኳᔕ೬ᡏ SigmaPlot ଞჹ 65<n<301 ೽ϩԔጕ଺

рന٫‫ڄ‬ኧኳᔕǶӧа q=80% നࣁѨਏำࡋਔǴ‫܌‬ኳᔕр᎖౷ႝԣ(‹)ϐ‫س‬಍ё᎞

ࡋ ୒୧ǡୱ୷ୱ୲ୣ୫ (n)ኳᔕрϐБำԄ‫ ځ‬Rɼ1, ଶ ɼ0.9999(Ѥ௭ϖΕԿλኧᗺΠಃѤՏ)Ƕ

ؒ ġ 1, 0‫أ‬n‫أ‬65ġ

 ୒୧ǡୱ୷ୱ୲ୣ୫ (n)ġ
n) ଵǤ଴଴ଽଽି଴Ǥ଴ଵ଺୬ା൫ଽǤସହ଺ଵൈଵ଴షఱ ൯୬మ ିሺଶǤସହଽସൈଵ଴షళ ሻ୬య ା൫ଶǤଷ଼ଶଷൈଵ଴షభబ ൯୬ర
=ġ , 65<n<301 ġ
ଵି଴Ǥ଴ଵହ଼୬ାሺଽǤହଷଶଵൈଵ଴షఱ ሻ୬మ ିሺଷǤ଴ହହଽൈଵ଴షళ ሻ୬య ାሺ଻Ǥହଵ଻଴ൈଵ଴షభబ ሻ୬ర

ؒ ġ 0, n‫ؤ‬301 (6.7)ġ

კ 23 ᎖౷ႝԣ(Ni) 65<n<301 Ԕጕኳᔕ

47
6.3 ‫ځ‬Ѭத‫ـ‬Ѩਏ኱ྗё᎞ࡋϩ‫݋‬
‫ځ‬Ѭத‫ـ‬Ѩਏ኱ྗࣁ೛‫ۓ‬ႝԣ଼ந‫ ݩރ‬SOH ե‫ ܭ‬70%ਔࣁѨਏаϷ೛‫ۓ‬ႝԣ

଼ந‫ ݩރ‬SOH ե‫ ܭ‬60%ਔࣁѨਏǶ೛ q ࣁѨਏᖏࣚॶǴ྽к‫ܫ‬ႝԛኧ(n)‫ۓڰ‬ਔǴ

߾ёฝр‫س‬಍ё᎞ࡋ ୱ୷ୱ୲ୣ୫ (n) = Pr[q< ሺሻሿჹᔈ‫ޑ‬ᗺǴ٠Ъीᆉ n=1 Կ n=300 ਔ

‫سޑ‬಍ё᎞ࡋ ୱ୷ୱ୲ୣ୫ (n)Ǵ߾ёᛤᇙ࣬ჹ‫ޑ‬ё᎞ࡋԔጕǶკ 24 ࣁѤᅿᜪձႝԣ‫܌‬ᇙ

q=70%ਔӚᜪձ᎖౷ႝԣ ୱ୷ୱ୲ୣ୫ Πफ़Ԕጕǹკ 25 ࣁѤᅿᜪձႝԣ‫܌‬ᇙ q=60%ਔӚ

ᜪձ᎖౷ႝԣ ୱ୷ୱ୲ୣ୫ Πफ़ԔጕǶёаܴᡉ࣮‫ډ‬྽೛‫ ޑۓ‬q ॶΠफ़ਔӚᅿᜪ᎖౷ႝԣ

ѨਏԔጕ೿ܴᡉӛѓ౽ǴҭջѨਏ‫ޑ‬ਔ໔‫ߏۯ‬Ƕ

კ 24 q=70%ࣁѨਏΠё᎞ࡋϩ‫݋‬

კ 25 q=60%ࣁѨਏΠё᎞ࡋϩ‫݋‬

48
6.4 Ӛᜪձ᎖౷ႝԣϐѨਏϩ‫݋‬
྽ᇙ೷୘ᒧ᏷Αటᇙ೷‫ޑ‬᎖౷ႝԣᜪǴ߾໪೛‫ځۓ‬Ѩਏ኱ྗǴԜਔКၨӚᜪձ

᎖౷ႝԣԾ‫ޑي‬Ѩਏᖏࣚॶ(q)ᆶк‫ܫ‬ႝԛኧ(n)ջࣁ΋ख़ाፐᚒǶҁ࿯ϩձ೛‫ۓ‬Ѩਏ

ࣁ q=80%, q=70% , q=60% ਔǴаѤᅿᜪձ᎖౷ႝԣԾ‫࣬ي‬КǴඔᛤрӚԾё᎞ࡋ

ԔጕӧόӕѨਏ኱ྗ೛‫ۓ‬ΠϐᡂϯǶ

6.4.1 ᎖౷ႝԣ(LS)‫ܭ‬όӕ q ਔё᎞ࡋԔጕ

ϩձ೛‫ۓ‬Ѩਏࣁ q=80%, q=70% , q=60% ਔǴLS ᎖౷ႝԣё᎞ࡋԔጕǶLS ᎖౷

ႝԣࣁҁፕЎѤᅿႝԣ྽ύόፕ q ॶǴё᎞ࡋ߄౜ࣣࣁനৡ‫ޑ‬ǴԜ่݀ᆶ‫ځ‬к‫ܫ‬ႝ

ϐ૰ଏԔጕ่݀Μϩ࣬಄ǴLS ᎖౷ႝԣк‫ܫ‬ႝϐ૰ଏԔጕΠफ़Кଆ‫ځ‬дႝԣ‫׳‬уଥ

৘ǴӢԜ‫ܭ‬ё᎞ࡋϩ‫݋‬ਔҭԖၨৡ‫่݀ޑ‬Ƕ

კ 26 ᎖౷ႝԣ(LS)‫ܭ‬όӕ q ਔё᎞ࡋԔጕ

49
6.4.2 ᎖౷ႝԣ(CO)‫ܭ‬όӕ q ਔё᎞ࡋԔጕ

ϩձ೛‫ۓ‬Ѩਏࣁ q=80%, q=70% , q=60% ਔǴCO ᎖౷ႝԣё᎞ࡋԔጕǶҗ‫ܭ‬ό

ᛙ‫ރ៌ࢲۓ‬ᄊˆୟଶ ሺͲሻଆ‫ॶۈ‬ၨଯǴӧ n<30 ਔΠफ़൯ࡋܴᡉ q=80%߄౜ၨৡǴᒿ๱

ˆୟଶ ሺ݊ሻΠफ़Ǵቹៜк‫ܫ‬ႝԔጕ‫ޑ‬ୟଵ՜ୢ ॶࣁѤᅿᜪձ᎖౷ႝԣ྽ύനեǴк‫ܫ‬ႝϐ૰

ଏԔጕၨࣁᖿ጗Ǵࡺ‫ ܭ‬q=70%ᆶ q=60%ਔ೿Ԗၨ٫‫߄ޑ‬౜Ƕ

კ 27 ᎖౷ႝԣ(CO)‫ܭ‬όӕ q ਔё᎞ࡋԔጕ

6.4.3 ᎖౷ႝԣ(‫۽ܑ܂‬૛ )‫ܭ‬όӕ q ਔё᎞ࡋԔጕ

ϩձ೛‫ۓ‬Ѩਏࣁ q=80%, q=70% , q=60% ਔǴ‹ܱଶ᎖౷ႝԣё᎞ࡋԔጕǶˆୟଶ ሺͲሻ=0

ӢԜӧк‫ܫ‬ႝ n ΢ϲ‫ޑ‬ၸำ྽ύႝ৒ໆΠफ़൯ࡋၨؒԖܴᡉ‫ँޑ‬ฅ‫ׯ‬ᡂǴࡺόӕ q

ਔё᎞ࡋԔጕ࣬՟Ǵᜪ՟НѳՏ౽Ƕ

50
 კ 28 ᎖౷ႝԣ(‹ଶ )‫ܭ‬όӕ q ਔё᎞ࡋԔጕ

6.4.4 ᎖౷ႝԣ(Ni)‫ܭ‬όӕ q ਔё᎞ࡋԔጕ

ϩձ೛‫ۓ‬Ѩਏࣁ q=80%, q=70% , q=60% ਔǴNi ᎖౷ႝԣё᎞ࡋԔጕǶNi ᎖౷

ႝԣࣁҁፕЎѤᅿႝԣ྽ύόፕ q ॶǴё᎞ࡋ߄౜ࣣࣁനӳ‫ޑ‬ǴԜ่݀ᆶ‫ځ‬к‫ܫ‬ႝ

ϐ૰ଏԔጕ่݀Μϩ࣬಄ǴNi ᎖౷ႝԣк‫ܫ‬ႝϐ૰ଏԔጕΠफ़Кଆ‫ځ‬дႝԣ‫׳‬уѳ

጗ǴӢԜ‫ܭ‬ё᎞ࡋϩ‫݋‬ਔҭԖၨ٫‫่݀ޑ‬Ƕ

კ 29 ᎖౷ႝԣ(Ni)‫ܭ‬όӕ q ਔё᎞ࡋԔጕ

51
ಃΎക ߥ‫ຼڰ‬ය

੃຤‫ޣ‬ᜢ‫ޑݙ‬ନΑᜢ‫ݙ‬යఈк‫ܫ‬ႝԛኧ(n)ᆶё᎞ࡋϐ໔ᜢ߯ѦǴҭሡाᕕှ

ߥ‫ޑڰ‬ጄൎٰߥም੃຤‫ޑޣ‬ሡ‫؃‬Ϸ៾੻ǹаᇙ೷୘‫ࡋف‬Ǵᒿ๱ѱ൑ᝡ‫ݾ‬ཇٰཇᐟ

ਗ਼Ǵౢࠔߥ‫ڰ‬೴ᅌ‫ת‬ᄽ๱ख़ा‫فޑ‬ՅǴԜόё۹ຎ‫ޑ‬ՉᎍЋࢤǴӢࣁߕԖၨ٫ߥ‫ڰ‬

ࠨऊ‫ޑ‬ౢࠔჹሡ‫؃‬Ԗ‫ڈ‬ᐟ‫ޑ‬բҔǴᙖҗߥ‫ຼڰ‬ය‫҅ޑ‬ዴ೛‫ߦۓ‬຾ᇙ೷୘‫ޑ‬ᎍ୧‫ک‬ᖂ

៉Ǵ੝ձࢂӳ‫ڰߥޑ‬ᆢঅࡹ฼ёගϲଯࠔ፦ౢࠔ‫׎ޑ‬ຝǴ٠ӢԜԋࣁѱ൑ᝡ‫ޑݾ‬Ԗ

Κ‫ݓ‬ᏔǶฅԶߥ‫ڰ‬ӕਔΨ཮٬ቷ୘Ѹ໪ॄᏼᚐѦ‫ڰߥޑ‬ԋҁǴ‫܌‬аቷ୘ӧౢࠔ΢ѱ

ᆶߦᎍਔѸ໪ஒ‫ځ‬યΕ᏾ӝ฼ౣ‫ޑ‬ԵໆǴ‫ځ‬ύх֖ౢࠔߥ‫ڰ‬ǵౢࠔुሽ‫ک‬ғౢ฼ౣ

฻Ǵ۶Ԝ৲৲࣬ᜢǶӢԜǴቷ୘ऩགྷගϲճዎ൩όૈаൂ΋฼ౣբԵໆԶሡ଺᏾ӝ

‫ࡘޑ‬ԵǶࡺҁക࿯ӢԜҁക࿯‫ ܭ‬7.1 ௖૸Ӛᜪձ᎖౷ႝԣӧόӕ‫ޑ‬Ѩਏᖏࣚॶ(q)Π

‫ޑ‬යఈк‫ܫ‬ႝԛኧ(n)ǹ7.2 ࿯߾аߞᒘ୔໔և౜к‫ܫ‬ႝԛኧ(n)‫ۓڰ‬Π‫܌‬යఈ‫ޑ‬ႝԣ

଼ந‫ރ‬ᄊ(SOH)ጄൎǶ

7.1 ႝԣ଼நԿѨਏк‫ܫ‬ႝԛኧ
аத‫ޑـ‬᎖ႝԣѨਏᖏࣚॶ q=SOH=80%, q= SOH=70%, q=SOH=60%,Ǵीᆉр

Ӛᜪձ᎖౷ႝԣ‫܌‬ሡϐයఈѨਏк‫ܫ‬ႝԛኧǴග‫ٮ‬٬Ҕ‫ߥޣ‬ምǴӧ٬Ҕਔёаᕕှ

Ҟ߻ႝԣҞ߻ϐ٬Ҕ‫ݩރ‬аϷයఈк‫ܫ‬ႝԛኧǴ߄ 7 ӈрӚᜪձ᎖౷ႝԣᆶத‫ـ‬ϐ

Ѩਏᖏࣚॶ(q)ჹᔈΠ‫ޑ‬යఈк‫ܫ‬ႝԛኧǶ

߄ 7 ႝԣ଼நԿѨਏк‫ܫ‬ႝԛኧ

q\ Battery LS CO ‫۽ܑ܂‬૛ Ni

80% 21 61 90 178

70% 31 189 139 291

60% 69 ε‫ ܭ‬300 196 300

52
7.2 ‫ຼۓڰ‬යΠǴႝԣႝ৒ໆߥ‫୔ڰ‬໔
ନΑᕕှ‫ډ‬Ⴃය٬ҔԛኧѦǴ੃຤‫ޣ‬ҭ཮ᜢЈк‫ܫ‬ႝԛኧ(n)Πϐߞᒘ୔໔ዴჴ

ӦඓඝӚᜪձ᎖౷ႝԣёૈ‫ޑ‬ႝ৒ໆ୔໔ጄൎǴӢԜ‫ ܭ‬7.2.1 Ԗշ‫ܭ‬ᡣ੃຤‫ޣ‬ᕕှ

аߞЈНྗ 99%Πႝ৒ໆᚈ‫ߞ׀‬ᒘ୔໔ǹк‫ܫ‬ႝԛኧ n ‫ۓڰ‬ΠǴаߞЈНྗ 99% Ǵ

ᡉ๱Нྗ α =0.01 ёаள‫ ߄ډ‬8ǴӚᜪձ᎖౷ႝԣᆶк‫ܫ‬ႝԛኧჹᔈϐႝ৒ໆᚈ‫ߞ׀‬

ᒘ୔໔

კ 30 к‫ܫ‬ႝԛኧ n ‫ۓڰ‬ΠǴႝԣႝ৒ໆᚈ‫ߞ׀‬ᒘ୔໔

߄ 8 Ӛᜪձႝԣႝ৒ໆᚈ‫ߞ׀‬ᒘ୔໔

ൻᕉԛኧ\ႝԣ LS ۱‫۽‬ ‫۽ܑ܂‬૛ Ni

10 84%~94% 88%~97% 93%~100% 90%~100%

20 75%~86% 83%~92% 90%~100% 90%~100%

30 69%~79% 80%~89% 87%~100% 89%~100%

40 64%~74% 78%~87% 85%~97% 88%~100%

50 60%~70% 76%~85% 82%~95% 87%~99%

60 57%~67% 75%~84% 80%~93% 86%~98%

70 54%~64% 74%~83% 78%~90% 84%~97%

80 52%~62% 73%~82% 75%~88% 83%~95%

90 50%~60% 72%~82% 73%~86% 82%~94%

53
 ຏ 1Ǻ߄਱ύኧॶጄൎ߄Ңӧᐉື੝‫ޑۓ‬᎖౷ႝԣᅿᜪΠǴჹᔈᕵືк‫ܫ‬ႝԛ

ኧ(n)‫܌‬ள‫ ޑډ‬99%ႝԣ଼ந‫ރ‬ᄊ(SOH)ߞᒘ୔໔Ƕ

‫ܭ‬ᇙ೷୘ҥ൑ǴࣁΑा๏ᆶ੃຤‫ڰߥޣ‬ය໔ǴӢԜ཮ӧ‫ۓڰ‬к‫ܫ‬ႝԛኧ n ϐΠ

ुрനեႝ৒ໆॶǴӵԜٰߥም੃຤‫੻៾ޣ‬Ǵᡣᇙ೷୘ᕕှаߞЈНྗ 99%Πႝ৒

ໆൂ‫ߞ׀‬ᒘ୔໔Ǵӵ߄ 9 ‫܌‬ҢǴаߥ᛾ӧ੝‫ۓ‬٬ҔԛኧΠϐനեႝ৒ໆǶीᆉрӚ

ᜪձႝԣӧόӕ‫ޑ‬к‫ܫ‬ႝԛኧ(n)ΠǴ99%ߞЈНྗ Ǵᡉ๱Нྗ α =0.01ǴѰ‫׀‬ϐൂ

‫ߞ׀‬ᒘ୔໔Ƕ

კ 31 к‫ܫ‬ႝԛኧ n ‫ۓڰ‬ΠǴႝԣႝ৒ໆൂ‫ߞ׀‬ᒘ୔໔ཷ‫ۺ‬კ

54
 ߄ 9 Ӛᜪձႝԣႝ৒ໆѰ‫ߞ׀‬ᒘ୔໔

ൻᕉԛኧ\ႝ
LS CO ࢀ࢏ࡻ૛ Ni
ԣ

10 85%~100% 89%~100% 94%~100% 91%~100%

20 76%~100% 83%~100% 91%~100% 91%~100%

30 70%~100% 81%~100% 89%~100% 90%~100%

40 65%~100% 79%~100% 86%~100% 89%~100%

50 61%~100% 77%~100% 83%~100% 88%~100%

60 58%~100% 76%~100% 81%~100% 87%~100%

70 55%~100% 75%~100% 79%~100% 86%~100%

80 53%~100% 74%~100% 77%~100% 84%~100%

90 51%~100% 73%~100% 74%~100% 83%~100%

55
ಃΖകǵ่ፕᆶ҂ٰࣴ‫ز‬Бӛ

8.1 ่ፕ
ႝ৒ໆ‫ޑ‬૰ଏ཮Ꮴठౢࠔ‫ૈ܄‬Πफ़ǵၮբૈΚ഼ѨǵࣗԿΓ‫ي‬Ӽӄ‫ޑ‬Ӓ্ǴӢ

ԜǴӧႝԣ‫ޑ‬ё᎞ࡋ௖૸ύǴዴϪᕕှႝԣ৒ໆ૰ଏᖿ༈࣬྽ख़ाǶԶ൩ႝԣё᎞

ࡋԶ‫ق‬Ǵჹ‫ܭ‬ႝԣᇙ೷୘ǴҁЎаଭёϻၸำࣴ‫ز‬ё᎞ࡋ᝼ᚒǴᙖаගᒬ‫زࣴೌמ‬

Γ঩όዴ‫܄ۓ‬Ȑхࡴୖኧᆶᕉნȑ
ǵტ‫ڮ‬ϩթǵё᎞ࡋ฻ᆶȨႝԣӼӄȩ‫ڀ‬Ԗଯࡋ‫ޑ‬

࣬ᜢǴᡣᇙ೷୘ᕕှႝԣტ‫ڮ‬૰ଏ‫ޑ‬ᖿ༈аϷႝԣტ‫ޑډڙ܌ڮ‬ज़‫ڋ‬Ǵයఈૈᡣ‫׳‬

ӭπำ೛ीΓ঩ஒё᎞ࡋཷ‫ۺ‬ЇҔԿ೛ीϐύǹԶჹ‫ܭ‬٬Ҕ‫ޣ‬Ǵ҅ዴඓඝႝԣౢࠔ

‫ޑ‬٬ҔБԄаϷкႝ฼ౣ߾ૈԖਏගϲႝԣტ‫ڮ‬аϷႝԣ‫ޑ‬٬Ҕਏ੻ǶӢԜҁࣴ‫ز‬

่ӝё᎞ࡋᆶଭёϻၸำ௖૸᎖ᚆη‫ރ‬ᄊόዴ‫ۓ‬ΠǴ᎖౷ႝԣϐ‫ܫ‬ႝ௃‫׎‬Ǵගр΋

‫ڀ‬ԖѤ‫ރ‬ᄊϐଭёϻၸำǴа C# ኗቪำԄаඔॊ᎖ႝԣ৒ໆᒿк‫ܫ‬ႝԛኧ૰ଏ‫ރ‬

‫ݩ‬Ǵ่݀ว౜ኳᔕ‫܌‬ளᆶ೸ၸୖԵЎ᝘ᇆ໣‫ޑډ‬ჴᡍኧᏵ࣬྽֍ӝǶ

࣬ၨ‫ܭ‬໺಍ࣴ‫ز‬аჴᡍБԄ௖૸ൂ΋‫׷‬਑‫ޑ‬ႝ৒ໆ૰ଏ௃‫׎‬ǴҁЎග‫ٮ‬΋঺х

֖ᐒ౗аϷໆϯё᎞ࡋ‫ޑ‬Кၨ୷ྗѳѠǴёа‫ޔ‬ௗКၨόӕ᎖౷ႝԣৡ౦ǶుΕ௖

૸όӕᜪձ᎖౷ႝԣ੝‫܄‬аϷႝ৒ໆ૰ଏ௃‫׎‬ǴᙖԜКၨ٬Ҕόӕཱུ҅‫ނ‬፦໔‫ޑ‬ৡ

౦ǶਥᏵኳࠠϩ‫่݀݋‬Ǵёа௢ፕ᎖౷ႝԣཱུ҅ύ‫ߎޑ‬ឦ਼ϯ‫ނ‬Ϸߎឦჹ᎖ᚆηவ

ࢲ៌‫ރ‬ᄊԿԝΫ‫ރ‬ᄊϐᐒ౗ૈԖᡉ๱‫ޑ‬फ़եǴԶԜᐒ౗،‫ۓ‬Α᎖౷ႝԣ‫ߏޑ‬යᛙ‫ۓ‬

‫܄‬ǹԶཱུ҅ύ‫ߎޑ‬ឦ਼ϯ‫ߎکނ‬ឦǴࢂᏤठόࢲ៌‫ރ‬ᄊ୧ р౜‫ޑ‬ёૈচӢǴ௢ፕࢂ

җ‫ܭ‬౷‫ߎک‬ឦϐ໔Ԗ๱மਗ਼‫࣬ޑ‬ϕբҔǴԶԜբҔค‫ݤ‬வᅹ౷‫س‬಍ύᢀჸ‫ډ‬ǶҁЎ

ᙖҗໆϯё᎞ࡋϩ‫݋‬௖૸όӕᜪձ᎖౷ႝԣӧόӕѨਏᖏࣚॶΠ‫ޑ‬ё᎞ࡋǴёа՘

᛾ߎឦ‫ނ‬፦‫ཱུ҅ܭ‬ᆶ౷ϯ‫ނ‬բҔ‫ޑ‬ዴёаமϯ᎖౷ႝԣ‫ޑ‬ტ‫ڮ‬ǴЀ‫ځ‬аᙻ୷݈ਏ݀

ന٫Ƕ

ҁЎჹ᎖౷ႝԣሦୱ஥ٰόӕ‫ޑ‬ϪΕຎ‫ف‬аϷࣁஒٰ‫ޑ‬຾৖ග‫ٮ‬ΑБӛǶයఈ

56
ૈ஥๏ᇙ೷୘ᆶወӧ੃຤‫ޣ‬ӄཥ‫ޑ‬ຎഁǶ

8.2 ҂ٰࣴ‫ز‬Бӛ
‫ڙ‬ज़‫܌ܭ‬ԏ໣‫ޑډ‬᎖ႝԣ‫ޑ‬ჴᡍኧᏵǴҁࣴ‫ز‬ճҔԖज़‫ޑ‬ၗ਑аଭёϻၸำᆶ

ё᎞ࡋ‫܌‬Ҕ‫୷ࣁۺཷޑ‬ᘵٰඔॊჴሞ‫ނޑ‬౛౜ຝǴӧҁЎύϐଭёϻኳࠠࢂଞჹ੝

‫ܫۓ‬ႝᕉნΠ‫ࡌ܌‬ᄬǴ೛‫ځۓ‬ѬᕉნӢηࣁதኧǴऩӧ‫ځ‬д‫ܫ‬ႝᕉნΠǴሡᙖҗ٣

Ӄ‫ޑ‬ჴᡍኧᏵǴќѦࡌᄬᙯ౽ંତǴঃऩ‫ڀ‬ഢ‫୼ى‬ϐჴᡍኧᏵǴёளऩυᅿόӕᕉ

ნΠ‫ޑ‬ᙯ౽ંତǴᙖҗӚᅿᙯ౽ંତ‫ޑ‬ಔӝёኳᔕӧᡂ୏ᕉნΠ‫ޑ‬ႝԣ୏ᄊ‫ܫ‬ႝၸ

ำǶ

‫ຼڰߥܭ‬ය᝼ᚒύǴ҂ٰёаࡌҥаౢࠔሽ਱Ϸߥ‫ࣁࡋߏڰ‬،‫ۓ‬ᡂኧ‫ޑ‬࿶ᔮኳ

ࠠǴѐ௖૸ӚঁᡂኧӵՖቹៜճዎǶҗ‫ڰߥܭ‬Ԗόӕ‫׎ޑ‬ԄǴӵֹӄߥ‫ڰ‬ǵ೽ϩߥ

‫ڰ‬ǵᚐѦߥ‫ڰ‬฻Ǵё௖૸όӕߥ‫ڰ‬௃ඳΠǴ੃຤‫ޣ‬ᆶᇙ೷୘όӕ‫ޑ‬฼ౣǴ٬੃຤‫ޣ‬

ளаന٫ϯԾρ‫ޑ‬ਏҔǴԶᇙ೷୘൩ૈ‫ډפ‬നεϯճዎ‫ޑ‬Ҟ኱ԄǴ٠‫؃‬ளᅈ‫ى‬Ҟ኱

‫ڰߥޑ‬ӝऊǶ

57
 ୖԵЎ᝘
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[26] ᎿО݅Ƕ᎖ᚆηႝԣൻᕉტ‫ڮ‬Ⴃෳኳࠠ‫زࣴޑ‬Ƕႝྍ‫زࣴೌמ‬යтǴ2008Ǵ43/5;!353.

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[27] ҴਔᓄǶ҉ᅶӕ‫؁‬ଭၲ‫س‬಍ϐё᎞ࡋຑ՗Ϸტ‫ڮ‬ႣෳǶ୯ҥѠ᡼εᏢᐒఓπำᏢࣴ‫܌ز‬

ᏢՏፕЎǴ3124Ƕ

[28] ቅৣำǶ᎖ႝԣ૰ଏኳࠠϐࡌᄬᆶനε‫ܫ‬ႝໆϩ‫݋‬Ƕᆵ᡼εᏢπ཰πำᏢࣴ‫܌ز‬ᏢՏፕ

ЎǴ 2014Ƕ

[29] ЎᆄܴǶᔈҔଭёϻ᜘ຑ՗᎖ႝԣ‫س‬಍ϐ SOCǶᆵ᡼εᏢᐒఓπำᏢࣴ‫܌ز‬ᏢՏፕЎǴ

2014Ƕ!

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61
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78
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!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/mbcfm3*<!
82
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/mbcfm2*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/oOvncfs*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy24*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy25*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy26*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy27*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy:*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy21*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy22*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy23*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy9*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy8*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy7*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy6*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy5*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy4*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy3*<!
!!!!!!!!!!!!uijt/Dpouspmt/Bee)uijt/ufyuCpy2*<!
!!!!!!!!!!!!uijt/Obnf!>!#Gpsn2#<!
!!!!!!!!!!!!uijt/Ufyu!>!#Gpsn2#<!
!!!!!!!!!!!!uijt/SftvnfMbzpvu)gbmtf*<!
!!!!!!!!!!!!uijt/QfsgpsnMbzpvu)*<!
!
!!!!!!!!~!
!
!!!!!!!!$foesfhjpo!
!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy2<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy3<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy4<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy5<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy6<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy7<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy8<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy9<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy:<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy21<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy22<!
83
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy23<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy24<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy25<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy26<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy27<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!oOvncfs<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/Mbcfm!mbcfm2<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/Mbcfm!mbcfm3<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/Mbcfm!mbcfm4<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy28<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy29<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy2:<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy31<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy32<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy33<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy34<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy35<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy36<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy37<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy38<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy39<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy3:<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy41<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy42<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!ufyuCpy43<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/Cvuupo!cvuupo2<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!sftvmuUfyu<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/Mbcfm!mbcfm5<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!gmjw2UfyuCpy<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/Mbcfm!mbcfm6<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!gmjw3UfyuCpy<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/Mbcfm!mbcfm7<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!gtUfyuCpy<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/Mbcfm!mbcfm8<!
!!!!!!!!qsjwbuf!Tztufn/Xjoepxt/Gpsnt/UfyuCpy!geUfyuCpy<!
!!!!~!
~!

84
2.Ӛᜪձႝԣ─к‫ܫ‬ႝԛኧᆶႝ৒ໆයఈॶჹྣ߄

MC-MI NMC-CO Coated SBFS570

1 1025ġ 1127ġ 820ġ 865ġ

2 1011ġ 1116ġ 826ġ 769ġ

3 998ġ 1105ġ 828ġ 769ġ

4 986ġ 1095ġ 827ġ 788ġ

5 974ġ 1085ġ 826ġ 805ġ

6 962ġ 1076ġ 824ġ 818ġ

7 951ġ 1068ġ 822ġ 826ġ

8 940ġ 1059ġ 820ġ 832ġ

9 929ġ 1052ġ 818ġ 836ġ

10 918ġ 1044ġ 815ġ 838ġ

11 908ġ 1037ġ 813ġ 839ġ

12 899ġ 1031ġ 811ġ 840ġ

13 889ġ 1025ġ 809ġ 840ġ

14 880ġ 1019ġ 807ġ 840ġ

15 871ġ 1013ġ 804ġ 839ġ

16 862ġ 1008ġ 802ġ 839ġ

17 854ġ 1003ġ 800ġ 838ġ

18 846ġ 998ġ 798ġ 837ġ

19 838ġ 993ġ 796ġ 836ġ

20 830ġ 989ġ 794ġ 835ġ

21 822ġ 985ġ 791ġ 834ġ

22 815ġ 981ġ 789ġ 833ġ

85
23 808ġ 977ġ 787ġ 832ġ

24 801ġ 974ġ 785ġ 831ġ

25 794ġ 970ġ 783ġ 830ġ

26 788ġ 967ġ 781ġ 830ġ

27 781ġ 964ġ 779ġ 829ġ

28 775ġ 961ġ 777ġ 828ġ

29 769ġ 958ġ 774ġ 827ġ

30 763ġ 955ġ 772ġ 826ġ

31 758ġ 952ġ 770ġ 825ġ

32 752ġ 950ġ 768ġ 824ġ

33 747ġ 947ġ 766ġ 823ġ

34 741ġ 945ġ 764ġ 822ġ

35 736ġ 943ġ 762ġ 821ġ

36 731ġ 941ġ 760ġ 820ġ

37 726ġ 938ġ 758ġ 819ġ

38 721ġ 936ġ 756ġ 818ġ

39 717ġ 934ġ 754ġ 817ġ

40 712ġ 932ġ 752ġ 816ġ

41 708ġ 931ġ 750ġ 815ġ

42 703ġ 929ġ 748ġ 814ġ

43 699ġ 927ġ 746ġ 813ġ

44 695ġ 925ġ 744ġ 812ġ

45 691ġ 924ġ 742ġ 811ġ

46 687ġ 922ġ 740ġ 810ġ

86
47 683ġ 921ġ 738ġ 809ġ

48 679ġ 919ġ 736ġ 808ġ

49 676ġ 918ġ 734ġ 807ġ

50 672ġ 916ġ 732ġ 806ġ

51 668ġ 915ġ 730ġ 805ġ

52 665ġ 913ġ 728ġ 804ġ

53 662ġ 912ġ 726ġ 804ġ

54 658ġ 911ġ 724ġ 803ġ

55 655ġ 909ġ 722ġ 802ġ

56 652ġ 908ġ 720ġ 801ġ

57 649ġ 907ġ 718ġ 800ġ

58 645ġ 905ġ 716ġ 799ġ

59 642ġ 904ġ 714ġ 798ġ

60 639ġ 903ġ 712ġ 797ġ

61 637ġ 902ġ 710ġ 796ġ

62 634ġ 901ġ 708ġ 795ġ

63 631ġ 900ġ 706ġ 794ġ

64 628ġ 898ġ 705ġ 793ġ

65 625ġ 897ġ 703ġ 792ġ

66 623ġ 896ġ 701ġ 791ġ

67 620ġ 895ġ 699ġ 790ġ

68 617ġ 894ġ 697ġ 789ġ

69 615ġ 893ġ 695ġ 788ġ

70 612ġ 892ġ 693ġ 788ġ

87
71 610ġ 891ġ 691ġ 787ġ

72 607ġ 890ġ 689ġ 786ġ

73 605ġ 889ġ 688ġ 785ġ

74 603ġ 888ġ 686ġ 784ġ

75 600ġ 887ġ 684ġ 783ġ

76 598ġ 886ġ 682ġ 782ġ

77 596ġ 885ġ 680ġ 781ġ

78 594ġ 884ġ 678ġ 780ġ

79 591ġ 883ġ 677ġ 779ġ

80 589ġ 882ġ 675ġ 778ġ

81 587ġ 881ġ 673ġ 777ġ

82 585ġ 880ġ 671ġ 776ġ

83 583ġ 879ġ 669ġ 776ġ

84 581ġ 878ġ 667ġ 775ġ

85 579ġ 877ġ 666ġ 774ġ

86 577ġ 876ġ 664ġ 773ġ

87 575ġ 875ġ 662ġ 772ġ

88 573ġ 874ġ 660ġ 771ġ

89 571ġ 873ġ 659ġ 770ġ

90 569ġ 872ġ 657ġ 769ġ

91 567ġ 872ġ 655ġ 768ġ

92 565ġ 871ġ 653ġ 767ġ

93 563ġ 870ġ 651ġ 766ġ

94 561ġ 869ġ 650ġ 766ġ

88
95 560ġ 868ġ 648ġ 765ġ

96 558ġ 867ġ 646ġ 764ġ

97 556ġ 866ġ 644ġ 763ġ

98 554ġ 865ġ 643ġ 762ġ

99 552ġ 864ġ 641ġ 761ġ

100 551ġ 863ġ 639ġ 760ġ

101 549ġ 862ġ 637ġ 759ġ

102 547ġ 862ġ 636ġ 758ġ

103 545ġ 861ġ 634ġ 757ġ

104 544ġ 860ġ 632ġ 757ġ

105 542ġ 859ġ 631ġ 756ġ

106 540ġ 858ġ 629ġ 755ġ

107 539ġ 857ġ 627ġ 754ġ

108 537ġ 856ġ 626ġ 753ġ

109 536ġ 855ġ 624ġ 752ġ

110 534ġ 855ġ 622ġ 751ġ

111 532ġ 854ġ 620ġ 750ġ

112 531ġ 853ġ 619ġ 749ġ

113 529ġ 852ġ 617ġ 749ġ

114 528ġ 851ġ 615ġ 748ġ

115 526ġ 850ġ 614ġ 747ġ

116 525ġ 849ġ 612ġ 746ġ

117 523ġ 848ġ 611ġ 745ġ

118 521ġ 848ġ 609ġ 744ġ

89
119 520ġ 847ġ 607ġ 743ġ

120 518ġ 846ġ 606ġ 742ġ

121 517ġ 845ġ 604ġ 742ġ

122 515ġ 844ġ 602ġ 741ġ

123 514ġ 843ġ 601ġ 740ġ

124 513ġ 842ġ 599ġ 739ġ

125 511ġ 842ġ 597ġ 738ġ

126 510ġ 841ġ 596ġ 737ġ

127 508ġ 840ġ 594ġ 736ġ

128 507ġ 839ġ 593ġ 735ġ

129 505ġ 838ġ 591ġ 735ġ

130 504ġ 837ġ 589ġ 734ġ

131 502ġ 836ġ 588ġ 733ġ

132 501ġ 836ġ 586ġ 732ġ

133 500ġ 835ġ 585ġ 731ġ

134 498ġ 834ġ 583ġ 730ġ

135 497ġ 833ġ 582ġ 729ġ

136 495ġ 832ġ 580ġ 729ġ

137 494ġ 831ġ 578ġ 728ġ

138 493ġ 831ġ 577ġ 727ġ

139 491ġ 830ġ 575ġ 726ġ

140 490ġ 829ġ 574ġ 725ġ

141 489ġ 828ġ 572ġ 724ġ

142 487ġ 827ġ 571ġ 723ġ

90
143 486ġ 826ġ 569ġ 723ġ

144 485ġ 825ġ 568ġ 722ġ

145 483ġ 825ġ 566ġ 721ġ

146 482ġ 824ġ 564ġ 720ġ

147 481ġ 823ġ 563ġ 719ġ

148 479ġ 822ġ 561ġ 718ġ

149 478ġ 821ġ 560ġ 717ġ

150 477ġ 820ġ 558ġ 717ġ

151 476ġ 820ġ 557ġ 716ġ

152 474ġ 819ġ 555ġ 715ġ

153 473ġ 818ġ 554ġ 714ġ

154 472ġ 817ġ 552ġ 713ġ

155 470ġ 816ġ 551ġ 712ġ

156 469ġ 816ġ 549ġ 711ġ

157 468ġ 815ġ 548ġ 711ġ

158 467ġ 814ġ 546ġ 710ġ

159 465ġ 813ġ 545ġ 709ġ

160 464ġ 812ġ 544ġ 708ġ

161 463ġ 811ġ 542ġ 707ġ

162 462ġ 811ġ 541ġ 706ġ

163 460ġ 810ġ 539ġ 706ġ

164 459ġ 809ġ 538ġ 705ġ

165 458ġ 808ġ 536ġ 704ġ

166 457ġ 807ġ 535ġ 703ġ

91
167 455ġ 806ġ 533ġ 702ġ

168 454ġ 806ġ 532ġ 701ġ

169 453ġ 805ġ 530ġ 701ġ

170 452ġ 804ġ 529ġ 700ġ

171 451ġ 803ġ 528ġ 699ġ

172 449ġ 802ġ 526ġ 698ġ

173 448ġ 802ġ 525ġ 697ġ

174 447ġ 801ġ 523ġ 697ġ

175 446ġ 800ġ 522ġ 696ġ

176 445ġ 799ġ 520ġ 695ġ

177 444ġ 798ġ 519ġ 694ġ

178 442ġ 798ġ 518ġ 693ġ

179 441ġ 797ġ 516ġ 692ġ

180 440ġ 796ġ 515ġ 692ġ

181 439ġ 795ġ 514ġ 691ġ

182 438ġ 794ġ 512ġ 690ġ

183 437ġ 794ġ 511ġ 689ġ

184 435ġ 793ġ 509ġ 688ġ

185 434ġ 792ġ 508ġ 688ġ

186 433ġ 791ġ 507ġ 687ġ

187 432ġ 790ġ 505ġ 686ġ

188 431ġ 790ġ 504ġ 685ġ

189 430ġ 789ġ 503ġ 684ġ

190 429ġ 788ġ 501ġ 684ġ

92
191 427ġ 787ġ 500ġ 683ġ

192 426ġ 786ġ 498ġ 682ġ

193 425ġ 786ġ 497ġ 681ġ

194 424ġ 785ġ 496ġ 680ġ

195 423ġ 784ġ 494ġ 679ġ

196 422ġ 783ġ 493ġ 679ġ

197 421ġ 782ġ 492ġ 678ġ

198 420ġ 782ġ 490ġ 677ġ

199 418ġ 781ġ 489ġ 676ġ

200 417ġ 780ġ 488ġ 675ġ

201 416ġ 779ġ 486ġ 675ġ

202 415ġ 778ġ 485ġ 674ġ

203 414ġ 778ġ 484ġ 673ġ

204 413ġ 777ġ 483ġ 672ġ

205 412ġ 776ġ 481ġ 672ġ

206 411ġ 775ġ 480ġ 671ġ

207 410ġ 775ġ 479ġ 670ġ

208 409ġ 774ġ 477ġ 669ġ

209 408ġ 773ġ 476ġ 668ġ

210 407ġ 772ġ 475ġ 668ġ

211 405ġ 771ġ 473ġ 667ġ

212 404ġ 771ġ 472ġ 666ġ

213 403ġ 770ġ 471ġ 665ġ

214 402ġ 769ġ 470ġ 664ġ

93
215 401ġ 768ġ 468ġ 664ġ

216 400ġ 768ġ 467ġ 663ġ

217 399ġ 767ġ 466ġ 662ġ

218 398ġ 766ġ 465ġ 661ġ

219 397ġ 765ġ 463ġ 660ġ

220 396ġ 764ġ 462ġ 660ġ

221 395ġ 764ġ 461ġ 659ġ

222 394ġ 763ġ 460ġ 658ġ

223 393ġ 762ġ 458ġ 657ġ

224 392ġ 761ġ 457ġ 657ġ

225 391ġ 761ġ 456ġ 656ġ

226 390ġ 760ġ 455ġ 655ġ

227 389ġ 759ġ 453ġ 654ġ

228 388ġ 758ġ 452ġ 654ġ

229 387ġ 758ġ 451ġ 653ġ

230 386ġ 757ġ 450ġ 652ġ

231 385ġ 756ġ 449ġ 651ġ

232 384ġ 755ġ 447ġ 650ġ

233 383ġ 754ġ 446ġ 650ġ

234 382ġ 754ġ 445ġ 649ġ

235 381ġ 753ġ 444ġ 648ġ

236 380ġ 752ġ 443ġ 647ġ

237 379ġ 751ġ 441ġ 647ġ

238 378ġ 751ġ 440ġ 646ġ

94
239 377ġ 750ġ 439ġ 645ġ

240 376ġ 749ġ 438ġ 644ġ

241 375ġ 748ġ 437ġ 644ġ

242 374ġ 748ġ 435ġ 643ġ

243 373ġ 747ġ 434ġ 642ġ

244 372ġ 746ġ 433ġ 641ġ

245 371ġ 745ġ 432ġ 641ġ

246 370ġ 745ġ 431ġ 640ġ

247 369ġ 744ġ 430ġ 639ġ

248 368ġ 743ġ 428ġ 638ġ

249 367ġ 742ġ 427ġ 638ġ

250 366ġ 742ġ 426ġ 637ġ

251 365ġ 741ġ 425ġ 636ġ

252 364ġ 740ġ 424ġ 635ġ

253 363ġ 739ġ 423ġ 635ġ

254 362ġ 739ġ 422ġ 634ġ

255 361ġ 738ġ 420ġ 633ġ

256 360ġ 737ġ 419ġ 632ġ

257 359ġ 736ġ 418ġ 632ġ

258 358ġ 736ġ 417ġ 631ġ

259 358ġ 735ġ 416ġ 630ġ

260 357ġ 734ġ 415ġ 629ġ

261 356ġ 733ġ 414ġ 629ġ

262 355ġ 733ġ 413ġ 628ġ

95
263 354ġ 732ġ 411ġ 627ġ

264 353ġ 731ġ 410ġ 626ġ

265 352ġ 730ġ 409ġ 626ġ

266 351ġ 730ġ 408ġ 625ġ

267 350ġ 729ġ 407ġ 624ġ

268 349ġ 728ġ 406ġ 623ġ

269 348ġ 728ġ 405ġ 623ġ

270 347ġ 727ġ 404ġ 622ġ

271 347ġ 726ġ 403ġ 621ġ

272 346ġ 725ġ 402ġ 620ġ

273 345ġ 725ġ 400ġ 620ġ

274 344ġ 724ġ 399ġ 619ġ

275 343ġ 723ġ 398ġ 618ġ

276 342ġ 722ġ 397ġ 618ġ

277 341ġ 722ġ 396ġ 617ġ

278 340ġ 721ġ 395ġ 616ġ

279 339ġ 720ġ 394ġ 615ġ

280 338ġ 719ġ 393ġ 615ġ

281 338ġ 719ġ 392ġ 614ġ

282 337ġ 718ġ 391ġ 613ġ

283 336ġ 717ġ 390ġ 612ġ

284 335ġ 717ġ 389ġ 612ġ

285 334ġ 716ġ 388ġ 611ġ

286 333ġ 715ġ 387ġ 610ġ

96
287 332ġ 714ġ 386ġ 610ġ

288 331ġ 714ġ 385ġ 609ġ

289 331ġ 713ġ 383ġ 608ġ

290 330ġ 712ġ 382ġ 607ġ

291 329ġ 712ġ 381ġ 607ġ

292 328ġ 711ġ 380ġ 606ġ

293 327ġ 710ġ 379ġ 605ġ

294 326ġ 709ġ 378ġ 605ġ

295 325ġ 709ġ 377ġ 604ġ

296 325ġ 708ġ 376ġ 603ġ

297 324ġ 707ġ 375ġ 602ġ

298 323ġ 706ġ 374ġ 602ġ

299 322ġ 706ġ 373ġ 601ġ

300 321ġ 705ġ 372ġ 600ġ

2.Ӛᜪձႝԣ─к‫ܫ‬ႝԛኧᆶᡂ౦ኧჹྣ߄

MC-MI NMC-CO Coated SBFS570

1 401 373 419 416

2 403 376 419 416

3 406 379 419 417

4 408 382 419 418

5 409 385 419 419

6 411 387 419 419

7 413 389 419 419

97
8 414 391 419 419

9 415 393 418 419

10 416 395 418 419

11 417 396 418 419

12 417 398 418 419

13 418 399 418 419

14 418 400 418 419

15 418 401 418 419

16 419 402 418 419

17 419 403 418 419

18 419 404 418 419

19 419 405 418 419

20 419 406 417 419

21 418 406 417 419

22 418 407 417 419

23 418 408 417 419

24 418 408 417 419

25 417 409 417 419

26 417 409 417 419

27 416 410 417 419

28 416 410 416 419

29 415 411 416 419

30 415 411 416 419

31 414 411 416 419

98
32 414 412 416 419

33 413 412 416 419

34 413 412 415 419

35 412 412 415 419

36 411 413 415 419

37 411 413 415 419

38 410 413 415 418

39 409 413 414 418

40 409 414 414 418

41 408 414 414 418

42 407 414 414 418

43 407 414 413 418

44 406 414 413 418

45 405 414 413 418

46 405 415 413 418

47 404 415 413 418

48 403 415 412 418

49 402 415 412 418

50 402 415 412 418

51 401 415 412 418

52 400 415 411 418

53 400 416 411 418

54 399 416 411 418

55 398 416 411 418

99
56 397 416 410 418

57 397 416 410 418

58 396 416 410 418

59 395 416 409 418

60 395 416 409 418

61 394 416 409 418

62 393 416 409 418

63 393 417 408 418

64 392 417 408 418

65 391 417 408 417

66 391 417 407 417

67 390 417 407 417

68 389 417 407 417

69 388 417 406 417

70 388 417 406 417

71 387 417 406 417

72 386 417 405 417

73 386 417 405 417

74 385 417 405 417

75 385 417 404 417

76 384 417 404 417

77 383 417 404 417

78 383 418 403 417

79 382 418 403 417

100
80 381 418 403 417

81 381 418 402 417

82 380 418 402 416

83 379 418 401 416

84 379 418 401 416

85 378 418 401 416

86 378 418 400 416

87 377 418 400 416

88 376 418 400 416

89 376 418 399 416

90 375 418 399 416

91 374 418 398 416

92 374 418 398 416

93 373 418 398 416

94 373 418 397 416

95 372 418 397 416

96 371 418 396 415

97 371 418 396 415

98 370 418 396 415

99 370 418 395 415

100 369 418 395 415

101 368 418 394 415

102 368 418 394 415

103 367 418 394 415

101
104 367 418 393 415

105 366 418 393 415

106 365 419 392 415

107 365 419 392 414

108 364 419 391 414

109 364 419 391 414

110 363 419 391 414

111 363 419 390 414

112 362 419 390 414

113 361 419 389 414

114 361 419 389 414

115 360 419 388 414

116 360 419 388 414

117 359 419 388 414

118 359 419 387 413

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120 357 419 386 413

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122 356 419 385 413

123 356 419 385 413

124 355 419 384 413

125 355 419 384 413

126 354 419 383 413

127 353 419 383 413

102
128 353 419 382 412

129 352 419 382 412

130 352 419 382 412

131 351 419 381 412

132 351 419 381 412

133 350 419 380 412

134 349 419 380 412

135 349 419 379 412

136 348 419 379 412

137 348 419 378 411

138 347 419 378 411

139 347 419 377 411

140 346 419 377 411

141 346 419 376 411

142 345 419 376 411

143 344 419 375 411

144 344 419 375 411

145 343 419 374 411

146 343 419 374 410

147 342 419 373 410

148 342 419 373 410

149 341 419 372 410

150 341 419 372 410

151 340 419 371 410

103
152 339 419 371 410

153 339 419 370 410

154 338 418 370 409

155 338 418 369 409

156 337 418 369 409

157 337 418 368 409

158 336 418 368 409

159 336 418 367 409

160 335 418 367 409

161 334 418 366 409

162 334 418 366 408

163 333 418 365 408

164 333 418 365 408

165 332 418 364 408

166 332 418 364 408

167 331 418 363 408

168 331 418 362 408

169 330 418 362 407

170 329 418 361 407

171 329 418 361 407

172 328 418 360 407

173 328 418 360 407

174 327 418 359 407

175 327 418 359 407

104
176 326 418 358 406

177 326 418 358 406

178 325 418 357 406

179 324 418 357 406

180 324 418 356 406

181 323 418 356 406

182 323 418 355 406

183 322 418 354 405

184 322 418 354 405

185 321 417 353 405

186 321 417 353 405

187 320 417 352 405

188 319 417 352 405

189 319 417 351 405

190 318 417 351 404

191 318 417 350 404

192 317 417 350 404

193 317 417 349 404

194 316 417 348 404

195 316 417 348 404

196 315 417 347 404

197 314 417 347 403

198 314 417 346 403

199 313 417 346 403

105
200 313 417 345 403

201 312 417 345 403

202 312 417 344 403

203 311 417 344 402

204 311 417 343 402

205 310 416 342 402

206 310 416 342 402

207 309 416 341 402

208 308 416 341 402

209 308 416 340 402

210 307 416 340 401

211 307 416 339 401

212 306 416 339 401

213 306 416 338 401

214 305 416 337 401

215 305 416 337 401

216 304 416 336 400

217 303 416 336 400

218 303 416 335 400

219 302 416 335 400

220 302 415 334 400

221 301 415 334 400

222 301 415 333 399

223 300 415 332 399

106
224 300 415 332 399

225 299 415 331 399

226 299 415 331 399

227 298 415 330 399

228 297 415 330 398

229 297 415 329 398

230 296 415 328 398

231 296 415 328 398

232 295 415 327 398

233 295 415 327 398

234 294 414 326 397

235 294 414 326 397

236 293 414 325 397

237 293 414 324 397

238 292 414 324 397

239 291 414 323 396

240 291 414 323 396

241 290 414 322 396

242 290 414 322 396

243 289 414 321 396

244 289 414 321 396

245 288 414 320 395

246 288 414 319 395

247 287 413 319 395

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248 287 413 318 395

249 286 413 318 395

250 286 413 317 395

251 285 413 317 394

252 284 413 316 394

253 284 413 315 394

254 283 413 315 394

255 283 413 314 394

256 282 413 314 393

257 282 413 313 393

258 281 412 313 393

259 281 412 312 393

260 280 412 311 393

261 280 412 311 392

262 279 412 310 392

263 279 412 310 392

264 278 412 309 392

265 277 412 309 392

266 277 412 308 392

267 276 412 308 391

268 276 412 307 391

269 275 411 306 391

270 275 411 306 391

271 274 411 305 391

108
272 274 411 305 390

273 273 411 304 390

274 273 411 304 390

275 272 411 303 390

276 272 411 302 390

277 271 411 302 389

278 271 411 301 389

279 270 410 301 389

280 270 410 300 389

281 269 410 300 389

282 268 410 299 389

283 268 410 298 388

284 267 410 298 388

285 267 410 297 388

286 266 410 297 388

287 266 410 296 388

288 265 409 296 387

289 265 409 295 387

290 264 409 295 387

291 264 409 294 387

292 263 409 293 387

293 263 409 293 386

294 262 409 292 386

295 262 409 292 386

109
296 261 409 291 386

297 261 409 291 386

298 260 408 290 385

299 260 408 290 385

300 401 373 419 416

110