配電系統為整個電力系統的末端，將電能由發電廠經由變壓器以及輸電饋線傳輸再經由配電系統分配給客戶。其運作之良窳，將影響電力供應之品質與服務的好壞。由於配電系統所涵蓋的範圍廣大，其元件間之關係複雜，以及電能傳遞過程所造成線路損失將降低系統運轉效率。藉由裝設電容器使系統正常運作，並可長期維持低損失及高可靠度之狀態是一種廣泛被使用的方法。
本論文提出多目標株落選擇演算法以解決具限制問題之多目標問題。株落選擇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以求解最佳化的問題，抗體及抗原可視為最佳化問題中的最佳解與目標函數。利用株落選擇及擴張與親和力成熟，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，而後期變動可增加抗體族群之歧異度，避免陷入局部最佳解的可能性。由於多目標函數間的單位大多不同難以整合，有鑑於此本研究提出交談式模糊滿足法，此方法優於傳統解法之處在於最佳化過程中不需經由對各目標函數定義權重因子即可依使用者所需求收尋並同時兼顧各目標函數的解。
本論文將電容器配置問題模式化成多目標規劃問題，結合株落選擇演算法與交談式模糊滿足法來決定如何配置電容器之裝設位置與容量的步驟。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。目標函數以模糊集合建構之，可利用模糊集合反映目標函數的不精確本質與合併多個在規劃時的需求。
本論文利用模擬軟體Matlab實現本文所提的演算法，並測試於IEEE 69-Bus之配電系統上與之前相關研究做比較，以證實本演算法之效能及實用性。

Typical distribution systems operate in a radial configuration which is supplied from power plant by substations and feeds to customers. The operation efficiency and service quality of distribution systems is indispensable. Distribution systems covered a very wide area with components are so big and complicated that contribute distribution line loss and 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.
This thesis presents a clone selection multi-objective algorithm to solve the constrained multi-objective problem. The clone selection algorithm simulates the operating relationship between the antigen and antibody in human immune system, which is in corresponding to the optimal solutions and objective functions of the optimization problem, to solve the optimization problem of reactive power and voltage control. Clone selection expansion and affinity maturation are applied to quick convergent speed and the global optimal solution can be achieved, and meta dynamics is applied to increase the diversity among antibodies to avoid the local optimal solution. Because the unit is different in multi-objective functions that hard for using tradition method to solve it. This study proposes the fuzzy-based interactive satisfied multi-objective method embedded with the conflict programming to the multi-objective optimal capacitor placement. This method is better than traditional method on that eliminates the need of any user-defined weight factor for aggregating all objectives. 
This thesis formulates the capacitor placement problem as a multi-objective problem, and combines clone selection algorithm with interactive fuzzy satisfied method to locate and determine the sizes of capacitors to be installed at the nodes of a radial distribution system under various loading conditions. 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. 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. 
Finally, this solution algorithm is implemented by Matlab, and tested on the IEEE 69-bus distribution system, as well as comparative studies are conducted on the test system with rather encouraging results. It proves that the proposed method is the most effective method to solve the optimal capacitor placement problem.

目  錄
目  錄	V
圖目錄	VII
表目錄	VIII
符號表	IX
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	7
2.1	簡介	7
2.2	負載潮流分析	7
2.2.1	傳統負載潮流分析	8
2.2.2	快速負載潮流解法	10
2.2.2.1	網路分支電流矩陣	11
2.2.2.2	網路阻抗矩陣	13
2.2.2.3	配電系統快速負載潮流演算法	15
第三章  株落選擇演算法	19
3.1	簡介	19
3.2	免疫系統	19
3.2.1	抗原	21
3.2.2	抗體	21
3.2.3	B細胞	22
3.2.4	T細胞	23
3.2.5	巨噬細胞	23
3.3	免疫系統特性	26
3.4	株落選擇演算法	27
3.4.1	株落選擇與記憶細胞	28
3.4.2	株落選擇演算法步驟	30
第四章  多目標最佳規劃	37
4.1	簡介	37
4.2	多目標函數最佳化問題	37
4.2.1	權重法	39
4.2.2	目標規劃法	40
4.2.3	妥協規劃法	41
4.2.4	交談式模糊滿足法	44
第五章  交談式株落選擇演算法於饋線上電容配置	46
5.1	 前言	46
5.2	 模糊表示法	46
5.3	 電容器規劃	48
5.3.1	購設電容器之成本函數	48
5.3.3	匯流排電壓最大變動量函數	51
5.4	 交談式株落選擇最佳電容器配置演算流程	54
5.5	 模擬測試	58
第六章  未來展望	70
6.1	結論	70
6.2	未來展望	72
參考文獻	73

圖目錄
圖 2.1：單一饋線配線系統	10
圖 2.2：配電系統示範例	11
圖 2.3：網路分支矩陣B之建立	13
圖 2.4：網路阻抗矩陣Z之建立	15
圖 2.5：配電系統快速負載潮流演算法	18
圖 3.1：抗原與抗體結合示意圖	21
圖 3.2：抗體組成結構示意圖	22
圖 3.3：免疫系統示意圖	25
圖 3.4：株落選擇示意圖	29
圖 3.5：免疫系統記憶特性示意圖	30
圖 3.6：株落選擇演算法流程	36
圖 4.1：兩目標問題之求解空間	42
圖 4.2：全域最佳非劣解求解空間	43
圖 4.3：全域最佳非劣解集合示意圖	44
圖 5.1：歸屬函數示意圖	47
圖 5.2：購設電容器成本歸屬函數	49
圖 5.3：能量損失成本歸屬函數	51
圖 5.4：匯流排電壓最大變動量歸屬函數	52
圖 5.5：饋線段及變壓器安全餘裕歸屬函數	54
圖 5.6：交談式演算流程圖	57
圖 5.7：69-BUS之配電系統	59

表目錄
表 5.1：電能成本以及持續時間之關係	57
表 5.2：69-BUS之配電系統之負載與各區饋線段資料（Part I）	59
表 5.3：69-BUS之配電系統之負載與各區饋線段資料（Part II）	60
表 5.4：進行第一次交談式演算法結果	62
表 5.5：裝設固定式電容器之位置及大小	63
表 5.6：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	63
表 5.7：裝設固定式電容器前後系統之最大最小電壓	64
表 5.8：裝設固定式電容器前後系統各負載程度損失	64
表 5.9：裝設固定式電容器前後系統負載餘裕	65
表 5.10：進行第二次交談式演算法結果	67
表 5.11：進行第三次交談式演算法結果	68

[1]	H.D. Chiang, J.C. Wang, O. Cockings, and H.D. Shin, “Optimal capacitor placements in distribution systems. I. A new formulation and the overall problem”, IEEE Trans. Power Delivery, Vol. 5, No. 2, pp. 634-642, April 1990.
[2]	H.D. Chiang, J.C. Wang, O. Cockings, and H.D. Shin, “Optimal capacitor placements in distribution systems. II. Solution algorithms and numerical results”, IEEE Trans. Power Delivery, Vol. 5, No. 2, pp. 643-649, April 1990.
[3]	M. Chis, M.M.A. Salama, and S. Jayaram, “Capacitor placement in distribution systems using heuristic search strategies,” IEE Proceedings- Generation, Transmission and Distribution, Vol. 144, No. 3, May 1997, pp. 225-230.
[4]	Y.C. Huang, H.T. Yang, and C.L. Huang, “Solving the capacitor placement problem in a radial distribution system using Tabu Search approach,” IEEE Trans. Power Systems, Vol. 11, No. 4, pp. 1868-1873, Nov. 1996.
[5]	S. Sundhararajan and A. Pahwa, “Optimal selection of capacitors for radial distribution systems using a genetic algorithm,” IEEE Trans. Power Systems, Vol. 9, No. 3, pp. 1499-1507, Aug. 1994.
[6]	C.T. Su, and C.C. Tsai, “A new fuzzy-reasoning approach to optimum capacitor allocation for primary distribution systems,” in Proceedings of 1996 IEEE on Industrial Technology Conference, 1996, pp.237-241.
[7]	V. Ajjarapu and Z. Albanna, “Application of genetic based algorithms to optimal capacitor placemen,” in Proceedings of the First International Forum on Applications of Neural Networks to Power Systems, July 1991, pp. 251-255.
[8]	張志翰，「利用模糊免疫多目標演算法之電容器最佳設置策略」，淡江大學電機工程學系，博士論文，民國96年6月。
[9]	簡靖陽，「配電系統操作最佳化之研究」，淡江大學電機工程學系，博士論文，民國89年6月。
[10]	張宗福，「應用蟻行混合差分進化法於配電系統運轉之研究」，國立中正大學電機工程研究所，博士論文，民國93年6月。
[11]	M.E. Baran, and F.F. Wu, “Optimal capacitor placement on radial distribution systems,” IEEE Trans. Power Delivery, Vol. 4, No. 1, pp. 725-734, Jan. 1989.
[12]	J.H. Teng, “A network-topology-based three-phase load flow for distribution systems,” in Proc. Natl. Sci. Counc. ROC, Vol. 24, No. 4, pp.259-264, 2000.
[13]	J.H. Teng and C.Y. Chang, “A novel and fast three-phase load flow for unbalanced radial distribution systems,” IEEE Trans. Power Systems, Vol. 17, No. 4, pp.1238-1244, Nov. 2002.
[14]	D. Dasgupta, Artificial immune systems and their applications. Berlin: Springer, 1999.
[15]	Leandro N. de Castro and Jonathan Timmis, Artificial immune systems : A new computational intelligence approach. London: Springer, 2002.
[16]	J.D. Farmer, N. H. Packard, and A. S. Perelson, “The immune system: adaptation and machine learning,” Physica, vol. 22D, pp. 187–204, 1986.
[17]	張嘉文，「以人工免疫學建構高穩定度入侵偵測演算法」，國立高雄第一科技大學運籌管理系，碩士論文，民國95年6月。
[18]	石慶男，「以多層支撐向量機結合株落選擇演算法建構電力變壓器故障診斷系統」，國立高雄應用科技大學電機工程學系，碩士論文，民國95年8月。
[19]	Y.T. Hsiao, “Multiobjective evolution programming method for feeder reconfiguration,” IEEE Trans. Power System, Vol. 19, No. 1, pp. 594-599, Feb. 2004.
[20]	V. Chankong and Y.Y. Haimes, “On the characterization of noninferior solutions of the vector optimization problem,” Automation, Vol. 18, No. 6, pp. 697-707, Nov. 1982.
[21]	P.P. Khargonekar and M.A. Rotea, “Multiple objective optimal control of linear systems: the quadratic norm case,” IEEE Trans. Automatic Control, Vol. 36, No. 1, pp. 14-24, Jan. 1991.
[22]	J.B. Yang and D. Li, “Normal vector identification and interactive tradeoff analysis using minimax formulation in multiobjective optimization,” IEEE Trans. Systems, Man and Cybernetics, Part A, Vol. 32, No. 3, pp. 305-319, May 2002.
[23]	K. Deb, Multi-objective optimization using evolutionary algorithms. Chichester: Wiley, 2001.
[24]	Y.L. Chen, “Weighted-norm approach for multiobjective VAr planning,” IEE Proceedings-Generation, Transmission and Distribution, Vol. 145, No. 4, pp. 369-374, July 1998.
[25]	U. Nangia, N.K. Jain, and C.L. Wadhwa, “Optimal weight assessment based on a range of objectives in a multiobjective optimal load flow study,” IEE Proceedings-Generation, Transmission and Distribution, Vol. 145, No. 1, pp. 65-69, Jan. 1998. 
[26]	馬誠韋，「解答多目標規劃的新方法-免疫系統法」，元智大學工業工程與管理學系，碩士論文，民國90年6月。
[27]	郭政謙，「應用多目標規劃法之配電自動化決策軟體」，國立台灣科技大學電機工程技術研究所，碩士論文，民國86年6月。
[28]	M. Sakawa and K. Yauchi, “An interactive fuzzy satisficing method for multiobjective nonconvex programming problems with fuzzy numbers through coevolutionary genetic algorithms,” IEEE Trans. Systems, Man and Cybernetics, Part B, Vol.31, No. 3, pp. 459-467, June 2001.
[29]	鄭仁福，「結合基因演算法與模擬退火法在饋線上電容配置」，國立台北科技大學電機工程系碩士班，碩士論文，民國89年6月。
[30]	李居昇，「配電系統最佳饋線重組與電容配置」，國立中正大學電機工程研究所，博士論文，民國91年6月。
[31]	S.J. Huang, "An immune-based optimization method to capacitor placement in a radial distribution system", IEEE Trans. Power Delivery, Vol. 15, No. 2, pp. 744-749, April 2000.