本論文提出適用於多重接地配電系統的三相諧波電力潮流分析技術及其被動式電力濾波器之最佳設計方法。首先，開發考量中性線與接地特性的三相四線式配電系統網路模型，基於電路解耦合概念和注入電流等效原理，將系統元件區分為串聯阻抗與並聯導納兩部分，串聯阻抗可利用圖脈理論建構出全系統的匯流排阻抗矩陣，而並聯導納則等效為匯流排注入電流，結合匯流排阻抗矩陣與匯流排注入電流即可推導本論文直接 電力潮流法，省去以往隱含式 法的矩陣求逆過程，提高計算效率。此外，本論文依搖擺匯流排是否考量接地阻抗，提出兩種處理中性線接地阻抗的方式，利用IEEE測試系統相互比較並說明兩者的優劣與使用時機。同時，與基於注入電流的前後掃描法和牛頓法進行收斂性能測試，驗證本文所提直接 法的疊代次數不受接地點數與接地阻抗大小的影響，收斂性能優於前述兩種演算法。本文研提之三相諧波電力潮流分析主要貢獻在於可詳細評估系統接地特性、負載條件、電容器投切與諧波成分等因素對系統中性點電壓、中性線電流、諧波失真和線路損失之具體影響。為改善中性線3次級諧波的問題，最後本論文結合非支配排序基因演算法II(Non-dominated Sorting Genetic Algorithm II, NSGAII)，進行多目標被動式電力濾波器設計，與過去方法的差別在於全面性地考量三相不平衡的諧波系統，而非將系統等效為單相，另外，也以實際常用的電容器容量作為最佳化濾波器的電容器選擇，因此設計出的濾波器能滿足三相系統的諧波限制且更貼近實務應用。

The main purpose of this thesis is to develop a three-phase harmonic power flow and its passive power filter design for multi-grounded four-wires distribution systems. Firstly, the network model of three-phase four-wire power distribution system considering the neutral line and grounding characteristics is developed. Based on the circuit decoupling concept and the injection current equivalent principle, the system components are divided into two parts: series impedance and parallel conduction. The series impedance can be used to construct the system bus impedance matrix by the graph theory, and the parallel admittance are equivalent to the bus injection currents.
The direct power flow method in this thesis is derived by bus impedance matrix and bus injection currents, without bus admittance matrix inversion process of the past implicit method, and the calculation efficiency is improved. In addition, two methods to deal with the neutral grounding impedance in power flow are proposed according to the swing bus grounding impedance. To compare pros and cons in these two methods, IEEE test systems are used. At the same time, the convergence performance of the proposed method is compared with the forward-backward sweep method and Newton method based on the current injection principle. The iteration number of the proposed method is not affected by the number of grounding points and grounding impedances, and the convergence performance is better than the above mentioned two methods.
The main contribution of the three-phase harmonic power flow analysis proposed in this thesis is that it can evaluate the influence of the system neutral voltage, neutral current, harmonic distortion and line loss by system grounding characteristics, load conditions, capacitor switching and harmonic components in detail. Finally, the non-dominated sorting genetic algorithm II (NSGAII) is combined to design the passive power filter to suppress the problem of triplen harmonics in the neutral line.
The difference from the past method is comprehensive consideration of three-phase unbalanced harmonic system, rather than a single-phase harmonic system. Furthermore, the actual capacitor capacity is used as the capacitor selection for optimizing passive filter. Therefore, the designed filter can satisfy all harmonic limits in the three-phase system.

[1] 李坤賢, "配電饋線中性線電流偏高問題成因探討與改善策略," 碩士, 電機工程研究所, 國立中正大學, 嘉義縣, 2003.
[2] R. M. Ciric, L. F. Ochoa, and A. Padilha, "Power flow in distribution networks with earth return," International Journal of Electrical Power & Energy Systems, vol. 26, no. 5, pp. 373-380, 2004/06/01/ 2004.
[3] R. M. Ciric, A. P. Feltrin, and L. F. Ochoa, "Power flow in four-wire distribution networks-general approach," IEEE Transactions on Power Systems, vol. 18, no. 4, pp. 1283-1290, 2003.
[4] M. J. E. Alam, K. M. Muttaqi, and D. Sutanto, "A Three-Phase Power Flow Approach for Integrated 3-Wire MV and 4-Wire Multigrounded LV Networks With Rooftop Solar PV," IEEE Transactions on Power Systems, vol. 28, no. 2, pp. 1728-1737, 2013.
[5] 高元海, 王淳, 辛建波, 劉愛國, 陳瑛, "計及接地阻抗及含多種分散式電源的中低壓配電網三相電力潮流計算(一)：模型," 中國電機工程學報, vol. 36, pp. 2619-2627, 2016.
[6] D. R. R. Penido, L. R. d. Araujo, S. Carneiro, J. L. R. Pereira, and P. A. N. Garcia, "Three-Phase Power Flow Based on Four-Conductor Current Injection Method for Unbalanced Distribution Networks," IEEE Transactions on Power Systems, vol. 23, no. 2, pp. 494-503, 2008.
[7] E. R. Collins and J. Jiang, "Analysis of Elevated Neutral-to-Earth Voltage in Distribution Systems With Harmonic Distortion," IEEE Transactions on Power Delivery, vol. 24, no. 3, pp. 1696-1702, 2009.
[8] A. M. Variz, J. L. R. Pereira, S. Carneiro, and P. G. Barbosa, "Harmonic analysis of the power distribution Neutral-to-Earth Voltage (NEV) test case using four-wire three-phase harmonic current injection method," in 2009 IEEE Power & Energy Society General Meeting, 2009, pp. 1-7.
[9] R. Horton, W. G. Sunderman, R. F. Arritt, and R. C. Dugan, "Effect of line modeling methods on neutral-to-earth voltage analysis of multi-grounded distribution feeders," in 2011 IEEE/PES Power Systems Conference and Exposition, 2011, pp. 1-6.
[10] C. Tsai-Hsiang and Y. Wen-Chih, "Analysis of multi-grounded four-wire distribution systems considering the neutral grounding," IEEE Transactions on Power Delivery, vol. 16, no. 4, pp. 710-717, 2001.
[11] J. Csatár and A. Dan, Neutral Voltage Comparison of Different Grounding Configurations and Calculation Methods in Multi-Grounded Low Voltage Network. 2017, pp. 77-81.
[12] J. Hurng-Liahng, W. Jinn-Chang, W. Kuen-Der, C. Wen-Jung, and C. Yi-Hsun, "Analysis of zig-zag transformer applying in the three-phase four-wire distribution power system," IEEE Transactions on Power Delivery, vol. 20, no. 2, pp. 1168-1173, 2005.
[13] P. Enjeti, W. Shireen, P. Packebush, and I. Pitel, "Analysis and design of a new active power filter to cancel neutral current harmonics in three phase four wire electric distribution systems," in Conference Record of the 1993 IEEE Industry Applications Conference Twenty-Eighth IAS Annual Meeting, 1993, pp. 939-946 vol.2.
[14] B. Singh, P. Jayaprakash, and D. P. Kothari, "A T-Connected Transformer and Three-leg VSC Based DSTATCOM for Power Quality Improvement," IEEE Transactions on Power Electronics, vol. 23, no. 6, pp. 2710-2718, 2008.
[15] C. A. Quinn, N. Mohan, and H. Mehta, "A four-wire, current-controlled converter provides harmonic neutralization in three-phase, four-wire systems," in Proceedings Eighth Annual Applied Power Electronics Conference and Exposition, 1993, pp. 841-846.
[16] P. Salmeron, J. C. Montano, J. R. Vazquez, J. Prieto, and A. Perez, "Compensation in nonsinusoidal, unbalanced three-phase four-wire systems with active power-line conditioner," IEEE Transactions on Power Delivery, vol. 19, no. 4, pp. 1968-1974, 2004.
[17] G. Escobar, A. A. Valdez, R. E. Torres-Olguin, and M. F. Martinez-Montejano, "A Model-Based Controller for A Three-Phase Four-Wire Shunt Active Filter With Compensation of the Neutral Line Current," IEEE Transactions on Power Electronics, vol. 22, no. 6, pp. 2261-2270, 2007.
[18] 楊文治, "各種接地方式配電系統之運轉特性研究," 博士, 電機工程系, 國立臺灣科技大學, 台北市, 2000.
[19] Electrical Power System Quality. McGraw-Hill, 2012.
[20] 江榮城, 電力品質. 全華圖書股份有限公司, 2012.
[21] 王耀諄, 電力系統品質. 新文京開發出版股份有限公司, 2005.
[22] 王耀諄, 電力品質. 高立圖書有限公司, 2005.
[23] S. Mekhamer, A. Abdelaziz, and S. Ismael, Technical Comparison of Harmonic Mitigation Techniques for Industrial Electrical Power Systems. 2012.
[24] N. He, D. Xu, and L. Huang, "The Application of Particle Swarm Optimization to Passive and Hybrid Active Power Filter Design," IEEE Transactions on Industrial Electronics, vol. 56, no. 8, pp. 2841-2851, 2009.
[25] "IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems," IEEE Std 519-2014 (Revision of IEEE Std 519-1992), pp. 1-29, 2014.
[26] "IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems," IEEE Std 519-1992, pp. 1-112, 1993.
[27] Z. Tongxin, E. B. Makram, and A. A. Girgis, "Power system transient and harmonic studies using wavelet transform," IEEE Transactions on Power Delivery, vol. 14, no. 4, pp. 1461-1468, 1999.
[28] A. Medina and N. Garcı́a, "Fast time domain computation of the periodic steady-state of systems with nonlinear and time-varying components," International Journal of Electrical Power & Energy Systems, vol. 26, no. 8, pp. 637-643, 2004/10/01/ 2004.
[29] K. L. Lian and T. Noda, "A Time-Domain Harmonic Power-Flow Algorithm for Obtaining Nonsinusoidal Steady-State Solutions," IEEE Transactions on Power Delivery, vol. 25, no. 3, pp. 1888-1898, 2010.
[30] J. Teng and C. Chang, "Backward/Forward Sweep-Based Harmonic Analysis Method for Distribution Systems," IEEE Transactions on Power Delivery, vol. 22, no. 3, pp. 1665-1672, 2007.
[31] N.-C. Yang and M.-D. Le, "Loop frame of reference based harmonic power flow for unbalanced radial distribution systems," International Journal of Electrical Power & Energy Systems, vol. 77, pp. 128-135, 2016/05/01/ 2016.
[32] J.-H. Teng, S.-H. Liao, and R.-C. Leou, Three-Phase Harmonic Analysis Method for Unbalanced Distribution Systems. 2014, pp. 365-384.
[33] 王星華, 余欣梅, 廣東工業大學自動化學院, 廣東省電力設計研究院系統規劃部, "諧波電力潮流建模及求解演算法研究綜述," (in 簡體中文), 電氣應用, no. 2008年 02, pp. 4-9, 2008.
[34] W. Kersting, "Distribution System Modeling and Analysis," 2007.
[35] T. Chen, M. Chen, K. Hwang, P. Kotas, and E. A. Chebli, "Distribution system power flow analysis-a rigid approach," IEEE Transactions on Power Delivery, vol. 6, no. 3, pp. 1146-1152, 1991.
[36] T. Gonen, "Electric Power Distribution Engineering, Third Edition," (in English), 2014.
[37] T.-H. Chen, W. C. Yang, T. Y. Guo, and G. C. Pu, Modeling and analysis of asymmetrical three-phase distribution transformer banks with mid-tap connected to the secondary neutral conductor. 2000, pp. 83-89.
[38] A. Arsoy and P. F. Ribeiro, Modeling and Simulation of Power System Harmonics. IEEE, 1999.
[39] R. Burch et al., "Impact of aggregate linear load modeling on harmonic analysis: a comparison of common practice and analytical models," IEEE Transactions on Power Delivery, vol. 18, no. 2, pp. 625-630, 2003.
[40] "Modeling and simulation of the propagation of harmonics in electric power networks. I. Concepts, models, and simulation techniques," IEEE Transactions on Power Delivery, vol. 11, no. 1, pp. 452-465, 1996.
[41] "Modeling and simulation of the propagation of harmonics in electric power networks. II. Sample systems and examples," IEEE Transactions on Power Delivery, vol. 11, no. 1, pp. 466-474, 1996.
[42] 羅欽煌, 工業配電. 全華圖書, 2008.
[43] G. W. Stagg and A. H. E. Abiad, "Computer Methods In Power System Analysis," 1980.
[44] N. Yang, "Three-phase power flow calculations using direct ZBUS method for large-scale unbalanced distribution networks," IET Generation, Transmission & Distribution, vol. 10, no. 4, pp. 1048-1055, 2016.
[45] S. Herraiz, L. Sainz, and J. Clua, "Review of harmonic load flow formulations," IEEE Transactions on Power Delivery, vol. 18, no. 3, pp. 1079-1087, 2003.
[46] N.-C. Yang and M. D. Le, Three-Phase Harmonic Power Flow by Direct ZBUS Method for Unbalanced Radial Distribution Systems with Passive Power Filters. 2016.
[47] W. H. Kersting, "A three-phase unbalanced line model with grounded neutrals through a resistance," in 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, 2008, pp. 1-2.
[48] D. R. R. Penido, L. R. Araujo, S. Carneiro, and J. L. R. Pereira, "Solving the single-circuit NEV test case using the current injection full-newton power flow," in 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, 2008, pp. 1-7.
[49] W. H. Kersting, "Radial distribution test feeders," in 2001 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.01CH37194), 2001, vol. 2, pp. 908-912 vol.2.
[50] W. H. Kersting, "Radial distribution test feeders," IEEE Transactions on Power Systems, vol. 6, no. 3, pp. 975-985, 1991.
[51] 張輝, "三相四線制配電網路電力潮流模型與演算法研究," 重慶大學, 重慶大學, 2007年論文, 2007.
[52] N. Yang and T. Chen, "Dual Genetic Algorithm-Based Approach to Fast Screening Process for Distributed-Generation Interconnections," IEEE Transactions on Power Delivery, vol. 26, no. 2, pp. 850-858, 2011.
[53] 張英彬, "工業用戶大容量電力諧波濾波器之最佳規劃," 博士論文,電機工程系,臺灣科技大學,台北市, 2004.
[54] J. H. Holland, Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence (Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence.). Oxford, England: U Michigan Press, 1975, pp. viii, 183-viii, 183.
[55] 許博傑, "實數編碼與二位元編碼遺傳演算法之性能比較研究," 碩士, 機械工程系, 國立台灣科技大學, 台北市, 2000.
[56] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182-197, 2002.
[57] C. Chih-Ju, L. Chih-Wen, L. June-Yown, and L. Kune-Da, "Optimal planning of large passive-harmonic-filters set at high voltage level," IEEE Transactions on Power Systems, vol. 15, no. 1, pp. 433-441, 2000.
[58] A. B. Nassif, X. Wilsun, and W. Freitas, "An Investigation on the Selection of Filter Topologies for Passive Filter Applications," IEEE Transactions on Power Delivery, vol. 24, no. 3, pp. 1710-1718, 2009.
[59] Y. P. Chang, W. K. Tseng, and T. F. Tsao, "Application of combined feasible-direction method and genetic algorithm to optimal planning of harmonic filters considering uncertainty conditions," IEE Proceedings- Generation, Transmission and Distribution, vol. 152, no. 5, pp. 729-736, 2005.
[60] H. Na, X. Dianguo, and L. Huang, "The Application of Particle Swarm Optimization to Passive and Hybrid Active Power Filter Design," IEEE Transactions on Industrial Electronics, vol. 56, no. 8, pp. 2841-2851, 2009.
[61] N. C. Yang and M. D. Le, "Optimal design of passive power filters based on multi-objective bat algorithm and pareto front," Applied Soft Computing, vol. 35, pp. 257-266, Oct 2015.
[62] A. A. Eajal and M. E. El-Hawary, "Optimal Capacitor Placement and Sizing in Unbalanced Distribution Systems With Harmonics Consideration Using Particle Swarm Optimization," IEEE Transactions on Power Delivery, vol. 25, no. 3, pp. 1734-1741, 2010.