臺灣博碩士論文加值系統

近年來綠能(Green Power) 意識高漲，其中碳排放量和石油危機是兩個重要的
議題，電動車即是順應這股趨勢所發展的產物。電動車不可缺少的元件之一為其
電池，而由於鋰電池放電量大且具穩定、充放電效率高、循環壽命長、體積小等
優點，已逐漸成為電動車動力來源的主流。評估電動車之電池效率常用到SOH
(State of Health)與SOC (Stare of Charge)，其中有關SOC 電池電量的量測技術以庫
倫積分法(Coulomb Integral Method) 為主，由於其方便與精確等特性，已廣泛被
應用在電動車SOC 之量測，但現今尚未有技術能準確估測SOC，特別的，量測與
評估的不確定性常被忽略。就此，本研究針對庫倫積分法量測計算上的隨機誤差，
建立數學上的馬可夫模型(Markov Model) ，藉以評估電動車行駛過程中SOC 逐
時下降的趨勢，以及任意使用時間點，處於各不同狀態SOC 之機率。本研究依據
他人實驗所得之電壓、放電量等數據，建立馬可夫模型，並考量電池出廠時的電
壓隨機變異性，以及電池在特定條件下充放電循環過程中老化衰減之隨機性，得
到鋰單電池在各使用時間點電量用盡之機率，最後再應用系統可靠度理論，推演
討論電池模塊(Battery Pack) 之 SOC。本研究所提出的方法能簡單有效模擬估算
真實環境下電池系統動態放電之SOC，並透過馬可夫分析模型得到各使用時間點
電量耗盡的機率，提供製造廠商進行符合ISO26262 等規範所需之風險評估。

With the growing consciousness of green power in recent years, the emissions of
carbon dioxide and oil crisis have been two critical issues. The electric vehicle is one of
many products developed with this trend. Batteries are indispensable to electric vehicles.
In particular, lithium batteries have gradually become the main power sources of electric
vehicles for the merits such as the stability and high efficiency of discharge, long cycle
life, small size, etc. When it comes to the way to evaluate the efficiency of electric
vehicles, State of Health (SOH) and State of Charge (SOC) are often applied. The latter
is mainly based on Coulomb integral method, and its property of convenience and
precision is widely applied to the SOC estimation of electric vehicles. However, no
available techniques can thoroughly be applied to estimate SOC. Therefore, this
research aims to direct the random errors of the estimation of the Coulomb integral
method and establish a Markov model for assessing the exhaustion of SOC along with
any time of discharge. This research is based on the voltage and capacity data from the
reference to establish the Markov model and take random differences and aging of
batteries into account. By doing so, we can come to realize the possibility of any battery
exhaustion clearly and then apply the system reliability theory to estimate the SOC of
batteries pack. With this research, we can efficiently estimate the SOC of dynamic
discharge of battery systems, and through the Markov model obtain the probability
distribution of battery exhaustion at any time. The results can be used for manufacturing
companies to carry out risk assessment for standards such as ISO26262.

CONTENTS
口試委員會審定書....................................................................................................... #
誌謝............................................................................................................................... i
中文摘要...................................................................................................................... ii
ABSTRACT ................................................................................................................ iii
CONTENTS ................................................................................................................ iv
LIST OF FIGURES ..................................................................................................... vi
LIST OF TABLES ..................................................................................................... viii
第一章 緒論....................................................................................................... 1
1.1 前言……………………….. ....................................................................... 1
1.2 研究動機與目的........................................................................................ 1
1.3 文獻回顧.................................................................................................... 2
1.3.1 電池SOC 模型................................................................................. 3
1.3.2 電池SOH 模型................................................................................. 3
1.4 研究方法與流程........................................................................................ 4
1.5 論文架構.................................................................................................... 5
第二章 電池相關理論概述................................................................................ 7
2.1 電池工作原理及比較................................................................................. 7
2.2 電池SOC................................................................................................... 8
2.3 電池SOH................................................................................................... 9
2.4 電池模塊/系統......................................................................................... 10
第三章 可靠度與馬可夫鏈概論...................................................................... 14
v
3.1 可靠度相關理論...................................................................................... 14
3.1.1 可靠度簡介..................................................................................... 14
3.1.2 可靠度數理概論............................................................................. 15
3.1.3 系統可靠度..................................................................................... 20
3.2 馬可夫鏈.................................................................................................. 21
3.2.1 馬可夫鏈簡介................................................................................. 21
3.2.2 馬可夫模型之特殊性質.................................................................. 23
第四章 案例模擬與分析.................................................................................. 27
4.1 馬可夫模型建構與執行........................................................................... 27
4.2 電池之隨機差異...................................................................................... 29
4.3 電池之循環衰減...................................................................................... 29
4.4 電池系統可靠度...................................................................................... 30
4.5 可靠度分析.............................................................................................. 31
第五章 結論..................................................................................................... 53
REFERENCES ........................................................................................................... 55

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