本文提出一個曲折繞接線變壓器在二十四脈波電壓源變流器架構中，該曲折繞接線變壓器架構除了使系統之輸出入側具有隔離效果外，亦可抑制及消除24n±1次以外的諧波(n=1,2,3…)。因此，本文利用特定諧波消除脈波寬度調變的方法來控制所提系統架構中的變流器。該方法具低開關切換頻率、低切換損失並且可直接控制基本波及消除特定諧波成份，適用於對特定諧波成份具有抑制能力的設備及中、高功率場合。
一般特定諧波消技術在波形上通常規劃為四分之一半波對稱波形。而本文在波形上除了規劃四分之一半波對稱波形，控制其系統輸出電壓之基本波、消除第二十三、二十五、四十七以及第四十九次諧波外，另針對半波對稱波形進行探討及分析，進一步提升電力品質，並使得變流器操作在低切換頻率下，系統輸出電壓之最低次諧波為七十一次。相較於一般低開關切換頻率之電壓源變流器，輸出電壓具有較低之諧波及較高的電力品質。本文利用MATLAB分析與模擬，最後以實作驗證其可行性。

In this paper, a zig-zag transformer applied in the 24 pulse voltage source inverter is presented, the zig-zag transformer provides the isolation between the input and output side of the system, it can additionally suppress and eliminate harmonics except the 24n ± 1 orders(n=1,2,3…). Thus the selective harmonic elimination pulse width modulation (SHE-PWM) method is used to control the inverter in the proposed system. This method yields the advantage of low switching frequency, low switching losses, the direct control of the fundamental harmonic component, and the elimination for particular harmonics. So this method is highly suitable for the apparatus with suppression to specific harmonics in high power applications.
Furthermore, SHE techniques usually perform one quarter-wave symmetry. In addition to generate the one half-wave symmetry waveform, this thesis also control the fundamental of the output voltage in system, eliminating 23rd, 25th, 47th, and 49th harmonics. Discussion and analysis to the half-wave symmetrical waveforms is conducted in the thesis to further improve the power quality and permits the inverter being operated with low switching frequency. The lowest harmonic order left in the output voltage is 71st. Compared to those voltage source inverters with low switching frequency, the proposed scheme yields lower harmonic distortion and higher power quality in the output voltage. In this thesis, MATLAB analysis and simulation, and finally to verify the feasibility of implementation.

參考文獻
[1]Xiong Rui, Hao Wei, and Chen Jian, “A study of parallel operation control technique of DC/AC SPWM inverter,” in proc. IEEE PEDS’99, 1999, vol. 2, pp. 1027-1032.
[2]N. B. Chaudhari, S. S. Wekhande, S. S. Dhamse, and S. Dhambhare,“A low cost high performance SPWM inverter,” in proc. IEEE PEDS’99, 1999, vol. 2, pp. 1033-1036.
[3]Yaow-Ming Chen, Chih-Hung Hsieh, and Yuan-Ming Cheng, “Modified SPWM control schemes for three-phase inverters,” in proc. IEEE PEDS’01, 2001, vol. 2, pp. 651-656.
[4]Xiumei Yue, Xuejun Ma, and Hongliang Wang , “A conceit of unipolar N-multiple frequency SPWM and the main circuit topology,” in Conf. IEEE IPEMC’09, 2009, pp. 1531-1534.
[5]徐福三，「多階直流-交流功率轉換器架構與脈波寬度調變技術之發展」，博士學位之論文，國立台北科技大學，民國九十四年七月。
[6]Steffen Bernet, “Recent developments of high power converters for industry and traction applications,” IEEE Trans. Power Electron., vol. 15, no.6, pp. 1102-1115, Nov. 2000.
[7]Kazunori Hasegawa, Hirofumi Akagi, “A new DC-voltage -balancing circuit including a single coupled inductor for a five-level diode-clamped PWM inverter,” IEEE Trans .Ind. Applicat., vol. 47, no. 2, pp. 841-852, March-Appril. 2011.
[8]E. S. Deepak, C.S. Anil, S. Sanjay, C. Febi and K. R Sajina, “A novel multilevel inverter topology based on multi-winding multi-tapped transformers for improved wave shape requirements,” in Conf. IEEE IICPE’11 , 2011, pp.1-5.
[9]Feng Wang, Jianguo Jiang, “A novel static frequency converter based on multilevel cascaded H-bridge used for the startup of synchronous motor in pumped-storage power station,” Energy Conversion and Management 52, 2011, pp. 2085-2091.
[10]M. R. Banaeiy and E. Salary, “Analysis of a generalized symmetrical multilevel inverter,” World Scientic Publishing Company, Oct. 2011, vol. 20, no. 2, pp. 299-311.
[11]M. R. Banaei ,and E. Salary, “ New multilevel inverter with reduction of switches and gate driver,” Energy Conversion and Management 52 , 2011, pp.1129–1136.
[12]王子榮，「台灣電氣化鐵路諧波之研究」，逢甲大學電機工程學 系碩士學位論文，民國九十一年。
[13]Lei Wang, Zhigang Liu, Gang Zhang, and Lijun Diao, “A novel traction power supply system for urban rail transportation,” in Conf. IEEE VPPC’08, 2008, pp. 1-5.
[14]巫昇峰，「基於曲折繞接線變壓器利用特定諧波消除之三階層 反流器研製」， 國立台灣科技大學電機工程系碩士學位論文， 民國九十六年。
[15]劉彥中,「基於曲折繞接線變壓器利用特定諧波消除之多階層反流器研製」， 國立台灣科技大學電機工程系碩士學位論文，民國九十八年。
[16]黃清龍，「特定諧波消除以曲折繞接變壓器為基礎之多階層變 流器」，國立台灣科 技大學電機工程系碩士學位論文，民國九十九年。
[17]J. R. Espinoza, J. I. Guzmán, L. A. Morán, and R. P. Burgos,‘Selective harmonic elimination and current/voltage control in current/voltage-source topologies: a unified approach,’’ IEEE Trans. Ind.Electron., vol. 48, no. 1, pp. 71-81, Feb. 2001.
[18]L. Xu, and V. G. Agelidis, ‘‘A VSC transmission system using flying capacitor multilevel converters and selective harmonic elimination PWM control,’’ in Conf. IEEE IPEC’05, 2005, vol. 2, pp. 1176-1181.
[19]S. A. Dahidah, and V. G. Agelidis, ‘‘Selective harmonic elimination PWM control for cascaded multilevel voltage source converters: a generalized formula,’’ IEEE Trans. Power Electron., vol. 23, no. 4, pp. 1620-1630, July 2008.
[20]Q. Liang, Z. Hui, L. Kaipei, and Q. Liu, ‘‘An improved modulation of the selective harmonic elimination controlling,’’ in Conf. IEEE ICPST’06, 2006, pp. 1-5.
[21]A. I. Maswood, ‘‘PWM SHE switching algorithm for voltage source inverter,”in Conf. IEEE PEDS’06, 2006, pp. 1-4.
[22]N. V. Nho, and M. J. Youn, ‘‘A simple on-line SHE PWM with extension to six step mode in two-level inverters,” in Conf. IEEE PEDS’05, 2005, pp. 1417-1424.
[23]J. Sun, S. Beineke, and H. Grotstollen, ‘‘Optimal PWM based on real-time solution of harmonic elimination equations,’’ IEEE Trans. Power Electron., vol. 11, no. 4, pp. 612-621, July 1996.
[24]C. Zheng, B. Zhang and D. Qiu, “Solving switching angles for the inverter’s selective harmonic elimination technique with walsh function,” in Conf. IEEE ICEMS’05, 2005 , vol. 2, pp. 1366-1370.
[25]J. N. Chiasson, L. M. Tolbert, K. J. McKenzie and Z. Du, “A complete solution to the harmonic elimination problem,” IEEE Trans. Power Electron., vol. 19, no. 2, pp.491-499, March. 2004.
[26]Quan Chen, Qunjing Wang, Weidong Jiang, and Xiaofeng Du, “A real-time solution to the harmonic elimination equations for three-level inverter,” in Congress IEEE WCICA’06, 2006, pp. 676-680.
[27]廖瑞聰，「二項次效應混合型疊代法之研究」，國立中央大學土 木工程系碩士學位論文，民國九十一年。
[28]Bingjie Zhao, Xiaojie Wu, Xiao Fu, and Peng Dai,“A novel 12-pulse 3-level inverter for STATCOM using selective harmonic elimination modulation,” in Conf. IEEE APPEEC’10, 2010, pp. 1-5.
[29]A. R. Bakhshai, G. Joos, and P. Jain, “A novel single pulse and pwm var compensator for high power application,” in Conf. IEEE IAS’98, 1998, vol. 2, pp. 1385-1392.
[30]Aiguo Xu, and Shaojun Xie, “A multi-pulse structure based AC-DC/DC-AC PWM converter for high power application,” in Conf. IEEE ICIT’09, 2009, pp. 1-6.
[31]B. Geethalakshmi and P. Dananjayan, “An analytic approach to harmonic analysis of 48-pulse voltage source inverter,” in Conf. IEEE PEDS’07, 2007, pp. 417-422.
[32]T. Selim, and S. Mekhilef, “A quasi soft switching 48-pulse PWM inverter with closed loop current control for the realization of FACTS devices,” in Conf. IEEE AUPEC’08, 2008, pp. 1-6.
[33]J. Ghaisari, and A. Bakhshai, “Exact harmonics elimination in pwm multi-nodule converters,” in Conf. IEEE APEC’05, 2005, vol. 3, pp. 1845-1850.
[34]Derek A Paice, “Power electronic converter : multipiles methods for clean power,” New York:Wiley-IEEE Press, 1995.
[35]Muhammad H. Rashid, “Power electronics: circuits, devices, and applications,” New Jersey : Pearson Prentice Hall , 3rd ed., 2004.
[36]J. Rodriguez, Jih-Sheng Lai, and Fang Zheng Peng, “Multilevel inverter : a survey of topologies controls and applications,” IEEE Trans. Ind. Electron., vol. 49, no. 4, pp. 724-738, Aug. 2002.
[37]I. Rasoanarivo, J. P. Martin, and S. Pierfederici, “Improvement of EMI behavior of npc multilevel inverter without balancing the voltage boundaries of DC bank capacitors,” in Congress IEEE ECCE’10,2010, pp. 2320-2325.
[38]L. M. Tolbert, F. Z. Peng, and T. G. Habetler, “Multilevel PWM methods at low modulation indices,” IEEE Trans. Power Electron. , vol. 15, no. 4, pp. 719-725, July. 2000.
[39]L. M. Tolbert and T. G. Habetler, “Novel multilevel invertercarrier-based PWM method,” IEEE Trans. Ind. Applicat., vol. 35, no. 5, pp. 1098-1107, Sept.-Oct. 1999.
[40]M. F. Escalante, J. C. Vannier and A. Arzande, “Flying capacitor multilevel inverters and dtc motor drive applications,” IEEE Trans. Ind. Electron., vol. 49, no. 4, pp. 809-815, Aug. 2002.
[41]C. Hpcjgraf, R. Lasseter, D. Divan and T. A. Lipo, “Comparison of multilevel inverters for static var compensation,” in Conf. Rec. IEEE ISA’94, 1994, vol. 2, pp. 921-928.
[42]L. A. Tolbert, F. Z. Peng, T. Cunnyngham and J. N. Chiasson, “Charge control schemes for cascade multilevel converter in hybrid electric vehicles,” IEEE Trans. Ind. Electron., vol. 49, no. 5, pp. 1058-1064, Oct. 2002.
[43]A. K. Verma, P. R. Thakura, K. C. Jana, and G. Buja, “Cascaded multilevel inverter for hybrid electric vehicles,” in Conf. IEEE IICPE’11, 2011, pp. 1-6.
[44]Kartick Chandra Jana, Sujit Kumar Biswas, and Parasuram Thakura “A simple and generalized space vector PWM control of cascaded H-bridge multilevel inverters,” in Conf. IEEE ICIT’06, 2006, pp. 1281-1286.
[45]Amit Kumar Gupta, and Ashwin “A space vector PWM scheme for multilevel inverters based on two-level space vector PWM,” IEEE Trans. Ind. Electron., vol.53,no .5, pp. 1631-1639, Oct. 2006
[46]J. Napoles, J. I. Leon, R. Portillo, L.G. Franquelo, and M.A. Aguirre,” Selective harmonic mitigation technique for high power converters,” IEEE Trans. Ind. Electron., vol .57, no. 7, pp. 2315-2323, July. 2010.
[47]S. R. Pulikanti, M. S. A. Dahidah, and V. G. Agelidis, “Voltage balancing control of three-level active npc converter using SHE-PWM,” IEEE Trans. Power Delivery , vol. 26, no. 1, pp. 258-267, Jan. 2011.
[48]Jorge Pontt , Jose Rodriguez , and Rodrigo Huerta, “Mitigation of noneliminated harmonics of SHE-PWM three-level multipulse three phase active front end converters with low switching frequency for meeting standard IEEE-519-92,” IEEE Trans. Power Electron. vol. 19, no. 6, pp. 1594-1600, Nov. 2004.
[49]N. Flourentzou, and V. G. Agelidis “Harmonic performance of multiple sets of solutions of SHE-PWM for a 2-level vsc topology with fluctuating DC-link voltage,” in Conf. IEEE AUPEC’07, 2007, pp. 1-8.
[50]Wanmin Fei , Xinbo Ruan , and Bin Wu ,“Ageneralized formulation of quarter-wave symmetry SHE-PWM problems for multilevel inverters,” IEEE Trans. Power Electron. vol. 24, no. 7, pp. 1758-1766, July 2009.
[51]Wanmin Fei; Xiaoli Du, Bin Wu; “Ageneralized half-wave symmetry SHE-PWM formulation for multilevel voltage inverter,” in Conf. IEEE APEC’10, 2010, pp. 1732-1735.
[52]N. Mohan, T. M. Undeland, and W. P. Robbins, “Power electronics: converters, applications, and design,” New York: Wiley, 3rd ed., 1995.
[53]M.T. Hagh, H. Taghizadeh, and K. Razi, “Harmonic minimization in multilevel inverter using modified species-based particle swarm optimization,” IEEE Trans. Power Electron. vol. 24, no. 10, pp. 2259-2267, Oct. 2009.
[54]Hadi Saadat, ‘‘Power system analysis,” McGraw-Hill, 2nd ed.,2004.
[55]王耀諄，「電力品質 Electric Power Quality」，高立圖書有限公 司，2005.
[56]江榮城，「電力品質實務(一)」，全華科技圖書股份有限公司,第 二版.，2002.