電力系統包含發電系統、輸電系統、配電系統等三大部份。傳統配電系統運轉在輻射狀架構上，將電能由發電廠經由變壓器以及輸電饋線傳輸分配給各客戶。配電系統為電力系統之最下游，涵蓋層面遼闊，電力輸送從主變電所或二次變電所之主變壓器、饋線、分歧線及配電變壓器、接戶線、線路接頭甚至電表等等，都會造成線路損失，同時會降低系統運轉效率。在電力饋線上裝設電容器以補償虛功率是一種廣泛被使用的方法，不論在城市或者鄉村型配電系統，利用此方式可以達到電壓調整、電能損失降低、修正功率因數、以及系統備轉容量提升。
一般而言，電容器設置的問題可以視為在不同的負載條件下之輻射型配電系統上，決定其裝設電容器之大小以及裝設位置。本論文將電容器規劃問題化成多目標規劃問題。此外，文中亦設計被動式單通濾波器來改善配電饋線的諧波污染。在輻射型配電系統上考慮四個目標函數，包括最小化電容器建構之成本、能量損失之成本、匯流排電壓之變動量及最大化饋線段（及變壓器）的安全邊界。在受諧波污染輻射型配電系統上考慮四個目標函數，包括最小化電容器建構之成本、能量損失之成本、匯流排電壓之變動量及最小化匯流排電壓總諧波失真。目標函數都以模糊模式建構之，可利用模糊集合反映目標函數的不精確的本質和可合併多個在規劃時的需求。
本論文提出二階段免疫多目標演算法去解決具限制問題之多目標問題。類免疫演算法係利用模擬抗體與抗原在人體免疫系統內的運作模式作最佳化來求解虛功率與電壓控制最佳化的問題，抗體及抗原可看成相當於最佳化問題中的最佳解與目標函數。利用抗體族群相似程度之關係，增加抗體族群之歧異度，可避免陷入局部最佳解的可能性，使得在求解空間的搜尋過程中，快速收斂且找到全域妥協解。本論文提出使用妥協規劃法之模糊類免疫多目標演算法去解決多目標電容器最佳配置。此方法可得到一妥協解（柏拉圖解）之集合而不是任一個由單一目標聚集出的最佳解，決策者依其需求選擇其中一組解來使用。此外，本方法不需經由對各目標函數定義權重因子即可求得妥協解。
最後在一個實際系統上與之前相關研究做比較，最後證實這個演算法之效能及實用性。以69-BUS之配電系統模擬，求解加裝電容器補償前以及補償後，各目標函數變化的情況，結果證實本論文所提出之方法優於其他最佳化方法，是解決電容器問題的有效方法。

Power System consists of generation, transmission and distribution systems to deliver the power service to customers. Typical distribution systems operate in a radial configuration which is supplied from substations and feeds to distribution transformers. Distribution systems cover a very wide area with components such as main transformers, primary feeders, laterals, distribution transformers, low tension lines and meters. All these components contribute distribution line loss to deteriorate system operation efficiency. Numerous shunt capacitors are installed along distribution feeders to compensate for reactive power to regulate the voltage, reduce energy, correct the power factor, and release system capacity, for both urban and rural areas.
The general capacitor placement problem is to locate and determine the sizes of capacitors to be installed at the nodes of a radial distribution system under various loading conditions. This dissertation formulates the capacitor placement problem as a multi-objective problem, including operational requirements. Furthermore, the single-tuned filter design is also presented to improve the harmonic distortion of the distribution feeders. The problem formulation presented in radial distribution system considers four objectives including of minimizing the cost of installing capacitors, minimizing the real power loss, minimizing the deviation of the bus voltage, and maximizing the capacity margin of the feeders and the transformer. The problem formulation presented in distorted distribution networks considers four objectives including of minimizing the cost of installing capacitors, the real power loss, the deviation of the bus voltage, and the total harmonic distortion of the bus voltage. A new problem formulation model of all objective functions with fuzzy sets to reflect the imprecise nature of objectives and incorporate the multiple requirements on planning is presented. 
This dissertation presents a two-staged immune multi-objective method to solve the constrained multi-objective problem. The artificial immune algorithm simulates the operating relationship between the antigen and antibody in human immune system, which are in corresponding to the optimal solution and objective function of the optimization problem, to solve the optimization problem of reactive power and voltage control. The affinity among the antibodies is applied to increase the diversity among them to avoid the local optimal solution such that the quick convergent speed and the global optimal solution can be achieved. This dissertation proposes the fuzzy-based artificial immune multi-objective method embedded with the compromise programming to the multi-objective optimal capacitor placement. The proposed method finds a set of non-inferior (Pareto) solutions rather than any single aggregated optimal solution for the decision maker to choose one particular solution. Besides, this proposed method eliminated the need of any user-defined weight factor for aggregating all objectives. 
Finally, to demonstrate the effectiveness of the proposed method, comparative studies are conducted on an actual system with rather encouraging results. To find out the changes of each objective function between before and after the placement of capacitors, 69-BUS distribution system is used to test in this method. It proves that the proposed method is the most effective method to solve the optimal capacitor placement problem.

目 錄
淡江大學論文中文提要..................................I
淡江大學論文英文提要................................III
致謝辭............................................... V
目 錄................................................VI
圖目錄...............................................IX
表目錄..............................................XII
符號表..............................................XIV
第一章 簡介.......................................... 1
1.1 研究動機......................................... 1
1.2 研究背景......................................... 2
1.3 研究內容......................................... 4
1.4 研究概要......................................... 5
第二章 電力饋線潮流分析.............................. 8
2.1 簡介............................................. 8
2.2 基頻負載潮流分析................................. 8
2.2.1 傳統負載潮流分析............................... 9
2.2.2 快速負載潮流解法.............................. 11
2.2.2.1 網路分支電流矩陣............................ 12
2.2.2.2 網路阻抗矩陣................................ 14
2.2.2.3 配電系統快速負載潮流演算法.................. 16
2.3 諧波負載潮流分析................................ 19
2.3.1 建立系統模型.................................. 19
2.3.1.1 負載模型.................................... 19
2.3.1.2 線性負載.................................... 20
2.3.1.3 非線性負載.................................. 21
2.3.1.4 傳輸線...................................... 22
2.3.1.5 電容器...................................... 23
2.3.1.6 濾波器...................................... 24
2.3.2 諧波潮流分析.................................. 25
第三章 多目標免疫演算法............................. 28
3.1 多目標函數最佳化問題............................ 28
3.1.1 定義.......................................... 29
3.1.1.1 可行解區域.................................. 29
3.1.1.2 非劣解...................................... 29
3.1.1.3 全域非劣解.................................. 29
3.1.2 權重法........................................ 30
3.1.3 妥協規劃法.................................... 31
3.1.4 交談式模糊滿足法.............................. 36
3.2 免疫系統........................................ 36
3.2.1 免疫演算法.................................... 40
3.2.2 二階段多目標免疫演算法........................ 44
第四章 多目標免疫演算法於饋線上電容配置............. 51
4.1 前言............................................ 51
4.2 電容器規劃...................................... 51
4.2.1 購設電容器之成本函數.......................... 52
4.2.2 能量損失成本函數.............................. 54
4.2.3 匯流排電壓最大變動量函數...................... 56
4.2.4 饋線段及變壓器安全餘裕函數.................... 57
4.3 模擬測試........................................ 59
4.3.1 固定式電容器.................................. 63
4.3.2 混合式電容器.................................. 72
第五章 諧波污染饋線上電容配置....................... 82
5.1 前言............................................ 82
5.2 電容器規劃...................................... 82
5.2.1 購設電容器之成本函數.......................... 83
5.2.2 能量損失成本函數.............................. 84
5.2.3 匯流排電壓最大變動量函數...................... 86
5.2.4 諧波失真因數函數.............................. 88
5.3 模擬測試........................................ 90
5.3.1 固定式電容器.................................. 92
5.3.2 混合式電容器................................. 106
第六章 諧波污染饋線上濾波器配置.................... 120
6.1 前言........................................... 120
6.2 電容器規劃目標函數............................. 120
6.2.1 購設濾波器之成本函數......................... 121
6.2.2 能量損失成本函數............................. 122
6.2.3 匯流排電壓最大變動量函數..................... 124
6.2.4 諧波失真因數函數............................. 126
6.3 模擬測試....................................... 128
第七章 未來展望.................................... 142
7.1 結論........................................... 142
7.2 未來展望....................................... 144
參考文獻........................................... 145

圖目錄
圖2. 1 單一饋線配線系統.......................................................................... 11
圖2. 2 配電系統示範例.............................................................................. 12
圖2. 3 網路分支矩陣B 之建立................................................................. 14
圖2. 4 網路阻抗矩陣Z 之建立.................................................................. 16
圖2. 5 配電系統快速負載潮流演算法...................................................... 18
圖2. 6 並聯式RL 電路模型....................................................................... 20
圖2. 7 串聯式RL 電路模型....................................................................... 21
圖2. 8 諧波源模型...................................................................................... 21
圖2. 9 諧波潮流分析流程圖...................................................................... 27
圖3. 1 兩目標問題之求解空間.................................................................. 32
圖3. 2 全域最佳非劣解求解空間.............................................................. 34
圖3. 3 全域最佳非劣解示意圖.................................................................. 35
圖3. 4 免疫系統的示意圖.......................................................................... 39
圖3. 5 信息熵圖示...................................................................................... 41
圖3. 6 多目標免疫演算法流程.................................................................. 50
圖4. 1 購設電容器成本歸屬函數.............................................................. 53
圖4. 2 能量損失成本歸屬函數.................................................................. 55
圖4. 3 匯流排電壓最大變動量歸屬函數.................................................. 57
圖4. 4 饋線段及變壓器安全餘裕歸屬函數.............................................. 58
圖4. 5 69-BUS 之配電系統........................................................................ 60
圖4. 6 裝設固定式電容器前後系統電能損失成本、購設成本以及年成本.......................................... 65
圖4. 7 裝設固定式電容器前後系統之最大最小電壓.............................. 67
圖4. 8 裝設固定式電容器前後系統各負載程度損失.............................. 69
圖4. 9 裝設固定式電容器前後系統負載餘裕.......................................... 71
圖4. 10 裝設混合式電容器前後系統電能損失成本、購設成本以及年成本............................................................................................................. 75
圖4. 11 裝設混合式電容器前後系統之最大最小電壓............................ 77
圖4. 12 裝設混合式電容器前後系統各負載程度損失............................ 79
圖 4. 13 裝設混合式電容器前後系統負載餘裕........................................ 81
圖5. 1 購設電容器成本歸屬函數.............................................................. 84
圖5. 2 能量損失成本歸屬函數.................................................................. 86
圖5. 3 匯流排電壓最大變動量歸屬函數.................................................. 87
圖5. 4 諧波失真因數歸屬函數.................................................................. 89
圖5. 5 補償前系統各匯流排THD 及其限制值....................................... 91
圖5. 6 受諧波污染饋線上裝設固定式電容器前後系統電能損失成本、購設成本以及年成本................................................................................. 94
圖5. 7 受諧波污染饋線上裝設固定式電容器前後系統之最大最小電壓................................................................................................................. 96
圖5. 8 受諧波污染饋線上裝設固定式電容器前後系統各負載程度損失................................................................................................................. 98
圖5. 9 受諧波污染饋線上裝設固定式電容器前後系統總THD .......... 100
圖5. 10 受諧波污染饋線上裝設固定式電容器前後系統各匯流排THDv及其限制值（Part I）.......................................................................... 101
圖5. 11 受諧波污染饋線上裝設固定式電容器前後系統各匯流排THDv及其限制值（Part II）......................................................................... 102
圖5. 12 受諧波污染饋線上裝設混合式電容器前後系統電能損失成本、購設成本以及年成本........................................................................... 108
圖5. 13 受諧波污染饋線上裝設混合式電容器前後系統之最大最小電壓............................................................................................................... 110
圖5. 14 受諧波污染饋線上裝設混合式電容器前後系統各負載程度損失............................................................................................................... 112
圖5. 15 受諧波污染饋線上裝設混合式電容器前後系統總THD ........ 114
圖5. 16 受諧波污染饋線上裝設混合式電容器前後系統各匯流排THDv及其限制值（Part I） .......................................................................... 115
圖5. 17 受諧波污染饋線上裝設混合式電容器前後系統各匯流排THDv及其限制值（Part II）......................................................................... 116
圖6. 1 購設電容器成本歸屬函數............................................................ 122
圖6. 2 能量損失成本歸屬函數................................................................ 124
圖6. 3 匯流排電壓最大變動量歸屬函數................................................ 125
圖6. 4 諧波失真因數歸屬函數................................................................ 127
圖6. 5 受諧波污染饋線上裝設被動式單通濾波器前後系統電能損失成本、購設成本以及年成本................................................................... 130
圖6. 6 受諧波污染饋線上裝設被動式單通濾波器前後系統之最大最小
電壓....................................................................................................... 132
圖6. 7 受諧波污染饋線上裝設被動式單通濾波器前後系統各負載程度
損失....................................................................................................... 134
XI
圖6. 8 受諧波污染饋線上裝設被動式單通濾波器前後系統總THD .. 136
圖6. 9 受諧波污染饋線上裝設被動式單通濾波器前後系統各匯流排
THDv 及其限制值（Part I）............................................................... 137
圖6. 10 受諧波污染饋線上裝設被動式單通濾波器前後系統各匯流排THDv 及其限制值（Part II） ............................................................. 138

表目錄
表4. 1 電能成本以及持續時間之關係...................................................... 59
表4. 2 69-BUS 之配電系統之負載與各區饋線段資料（Part I）........... 61
表4. 3 69-BUS 之配電系統之負載與各區饋線段資料（Part II） ......... 62
表4. 4 裝設固定式電容器之位置及大小.................................................. 63
表4. 5 裝設固定式電容器前後系統電能損失成本、購設成本以及年成本................................................................................................................. 65
表4. 6 裝設固定式電容器前後系統之最大最小電壓.............................. 67
表4. 7 裝設固定式電容器前後系統各負載程度損失.............................. 69
表4. 8 裝設固定式電容器前後系統負載餘裕.......................................... 71
表4. 9 裝設混合式電容器之位置、大小及型式...................................... 73
表4. 10 裝設混合式電容器前後系統電能損失成本、購設成本以及年成本............................................................................................................. 75
表4. 11 裝設混合式電容器前後系統之最大最小電壓............................ 77
表4. 12 裝設混合式電容器前後系統各負載程度損失............................ 79
表4. 13 裝設混合式電容器前後系統 負載餘裕........................................ 81
表5. 1 受諧波污染饋線上裝設固定式電容器之位置及大小................. 92
表5. 2 受諧波污染饋線上裝設固定式電容器前後系統電能損失成本、購設成本以及年成本................................................................................. 94
表5. 3 受諧波污染饋線上裝設固定式電容器前後系統之最大最小電壓................................................................................................................. 96
表5. 4 受諧波污染饋線上裝設固定式電容器前後系統各負載程度損失................................................................................................................. 98
表5. 5 受諧波污染饋線上裝設固定式電容器前後系統總THD .......... 100
表5. 6 受諧波污染饋線上裝設固定式電容器前後系統各匯流排THDv
值（Part I） .......................................................................................... 103
表5. 7 受諧波污染饋線上裝設固定式電容器前後系統各匯流排THDv
值（Part II）......................................................................................... 104
表5. 8 受諧波污染饋線上裝設固定式電容器前後系統各匯流排THDv
值（Part III） ....................................................................................... 105
表5. 9 受諧波污染饋線上裝設混合式電容器之位置及大小............... 107
表5. 10 受諧波污染饋線上裝設混合式電容器前後系統電能損失成本、購設成本以及年成本........................................................................... 108
表5. 11 受諧波污染饋線上裝設混合式電容器前後系統之最大最小電壓
............................................................................................................... 110
表5. 12 受諧波污染饋線上裝設混合式電容器前後系統各負載程度損失
............................................................................................................... 112
表5. 13 受諧波污染饋線上裝設混合式電容器前後系統總THD ........ 114
表5. 14 受諧波污染饋線上裝設混合式電容器前後系統各匯流排THDv值（Part I） .......................................................................................... 117
表5. 15 受諧波污染饋線上裝設混合式電容器前後系統各匯流排THDv值（Part II）......................................................................................... 118
表5. 16 受諧波污染饋線上裝設混合式電容器前後系統各匯流排THDv值（Part III） ............................... ........................................................ 119
表6. 1 受諧波污染饋線上裝設單通濾波器之位置及其大小............... 129
表6. 2 受諧波污染饋線上裝設被動式單通濾波器前後系統電能損失成本、購設成本以及年成本................................................................... 130
表6. 3 受諧波污染饋線上裝被動式單通濾波器前後系統之最大最小電
壓........................................................................................................... 132
表6. 4 受諧波污染饋線上裝設被動式單通濾波器前後系統各負載程度
損失....................................................................................................... 134
表6. 5 受諧波污染饋線上裝設被動式單通濾波器前後系統總THD .. 136
表6. 6 受諧波污染饋線上裝設被動式單通濾波器前後系統各匯流排
THDv 值（Part I）............................................................................... 139
表6. 7 受諧波污染饋線上裝設被動式單通濾波器前後系統各匯流排
THDv 值（Part II） ............................................................................. 140
表6. 8 受諧波污染饋線上裝設被動式單通濾波器前後系統各匯流排
THDv 值（Part III） ............................................................................ 141

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