近日，因全球對電機驅動之需求扶搖直上；為追求低成本，高效率與高可靠度，電動機或者齒輪幫浦將由電壓轉換器來驅動。矩陣型轉換器(Matrix converter)將擔任此腳色，在電路架構不需要維持直流電壓的電容就可以達到輸出擁有更大功率的交流電壓。
本文將介紹一小體積、弦波電壓輸出暨電流輸入、雙向功率輸出且無須一笨重且擁有壽命限制之電容盡人皆知之轉換器—矩陣型轉換器。文章內容將提供矩陣型轉換器之開發包括PWM之控制方法、機台組件以及用來保護主轉換器之箝位電路來避免在錯誤的開關切換時造成損害。魚與熊掌之不可兼得，雖矩陣型轉換器擁有許多歷史上發展過之交流—交流轉換器的優點，但卻始終存在一令人為之詬病的缺失—低電壓轉換率使得轉換器之輸出電壓極為限制。將先使用模擬軟體(PLECS)來驗證PWM之方法之正確性，從模擬上較易檢查方法之錯誤並且加以改進，當模擬結果成功後即可在實際的實驗機台加以實現。為了擁有實際的實驗結果，實驗室將首先開發功率三千瓦的矩陣型轉換器，成為實驗室第一個矩陣型轉換器，將如履薄冰般細微的檢查所有實驗機台之細節已減少任何意外狀況。討論議題將從三相之平衡電壓開始確認PWM之方法與閉迴路控制可在實驗平台上實行，更進一步將期望可以在三相不平衡輸入電壓的情況下亦可透過文章所提供之方法輸出所期待之輸出電壓。

Recently, the electrical drive becomes more and more popular around the whole world, the electric motor or even gear pump in a single unit, for lower costs, it’s efficiency and more reliable to drive them with the power converter. The matrix converter can play this role which this converter doesn’t need a capacitor to deliver the AC power.
This thesis will present the integrated regenerative frequency converter which is different from the power inverter known before. The small volume, sinusoidal output voltage and input current with bidirectional power flow and the most important without any bulky, life time limited capacitor, known for the Matrix Converter. This thesis would introduce the development of the first matrix converter, including the PWM method, the test bench construction and the clamped circuit which apply to avoid the critical damage to the transistors. However the disadvantage of the matrix converter, the low voltage transfer ratio, will also discuss in the thesis. The PWM method and the control idea will be verified in the simulation which the PLECS is the simulation software used. If the modulation method success, the next step is going to realize the whole idea on a realistic test bench. A 3-kW matrix converter prototype will be built, for being the pioneer of the laboratory, every detail will be verified step by step very carefully in order to minimize the error of the test bench. It’s expected to do the research not only as the input voltage be three phase balanced, but also when the unbalanced voltage occurs, it’s more challenged to control matrix converter output voltage to be three phase balanced voltages under the unbalanced three phase voltage.

ABSTRACT i
ACKNOWLEDGMENTS ii
LIST OF TABLES v
LIST OF FIGURES vi
1 Introduction 1
1.1 Background 1
1.2 Basic concept of the matrix converter 3
1.3 Motivation of this study 4
1.4 Dissertation organization 5
1.5 Variable definition 6
2 Literature Review 7
2.1 Output voltage synthesis 7
2.2 Input current synthesis 9
2.3 Transfer ratio validation 12
2.4 Conclusion 13
3 Operation Principle 14
3.1 Continuous carrier base modulation 14
3.2 Sampling time 17
3.3 Switching execution 19
3.3.1 Switching limitation of matrix converter 19
3.3.2 Commutation method 21
3.3.2.1 Current commutation 21
3.3.2.2 Voltage commutation 26
3.4 Proposed switching method 31
3.4.1 Carrier waves 31
3.4.2 Voltage commutation 32
3.4.3 Current commutation 35
3.5 Commutation time compensation 40
3.6 Controller 48
3.6.1 Open loop voltage control 48
3.6.2 Closed loop current control 49
3.7 Clamped circuit design 53
3.8 Conclusion 55
4 Simulation 57
4.1 Open loop voltage test 57
4.2 Closed loop current test 62
4.3 Conclusion 68
5 Laboratory Experiment 69
5.1 Open loop voltage test 69
6 Summary 78
Appendix A Test Bench Construction 79
I Overview 79
II Power board 79
III Sensor board and Comparison 83
IV Protection board modification 87
V DSP and CPLD 89
VI PWM signals transmission path 92
Reference 95

[1] V. R. Gasiyarov, A. S. Maklakov and R. A. Lisovski, "Grid power control by medium voltage AC drives based on back-to-back converters," 2018 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus), Moscow, 2018, pp. 629-631.
[2] H. Jafari, M. Mahmoudi, A. Fatehi, M. H. Naderi and E. Kaya, "Improved power sharing with a back-to-back converter and state-feedback control in a utility-connected microgrid," 2018 IEEE Texas Power and Energy Conference (TPEC), College Station, TX, 2018, pp. 1-6.
[3] L. Helle, K. B. Larsen, A. H. Jorgensen, S. Munk-Nielsen, and F. Blaabjerg, “Evaluation of modulation schemes for three-phase to three-phase matrix converters,” IEEE Trans. Ind. Electron., vol. 51, no. 1, pp. 158–171, Feb. 2004.
[4] Young-Doo Yoon and Seung-Ki Sul, “Carrier-Based Modulation Technique for Matrix Converter,” IEEE trans. Power Electron., vol.32, no. 6, Nov. 2006
[5] M. Su et al., "Modified modulation scheme for three-level diode-clamped matrix converter under unbalanced input conditions," in IET Power Electronics, vol. 11, no. 8, pp. 1425-1433, 7 10. 2018
[6] J. Zhang, H. Yang, T. Wang, L. Li, D. G. Dorrell and D. D. C. Lu, "Field-oriented control based on hysteresis band current controller for a permanent magnet synchronous motor driven by a direct matrix converter," in IET Power Electronics, vol. 11, no. 7, pp. 1277-1285, 6 19. 2018.
[7] —, “Space vector modulated three-phase to three-phase matrix converter with input power factor correction,” IEEE Trans. Ind. Appl., vol.31, no. 6, pp. 1234–1246, Nov./Dec. 1995.
[8] D. Casadei, G. Grandi, G. Serra, and A. Tani, “Space vector control of matrix converters with unity input power factor and sinusoidal input/output waveforms,” in Proc. EPE Conf., 1993, vol. 7, pp. 170–175.
[9] D. Casadei, G. Serra, and A. Tani, “Reduction of the input current harmonic content in matrix converters under input/output unbalance,” IEEE Trans. Ind. Electron., vol. 45, no. 3, pp. 401–411, Jun. 1998.
[10] A. M. Hava, R. J. Kerkman, and T. A. Lipo, “Simple analytic and graphical methods for carrier-based PWM-VSI drives,” IEEE Trans.Power Electron., vol. 14, no. 1, pp. 49–61, Jan. 1999.D. W. Chung, J. S. Kim, and S. K. Sul, “Unified voltage modulation
[11] D. W. Chung, J. S. Kim, and S. K. Sul, “Unified voltage modulation technique for real-time three-phase power conversion,” IEEE Trans.Ind. Appl., vol. 34, no. 2, pp. 374–380, Mar./Apr. 1998.
[12] T. G. Habetler, F. Profumo, M. Pastorelli, and L. M. Tolbert, “Direct torque control of induction machines using space vector modulation,” IEEE Trans. Ind. Appl., vol. 28, no. 5, pp. 1045–1053, Sep./Oct. 1992.
[13] J. Mahlein, J. Igney, J. Weigold, M. Braun, O. Simon, “Matrix Converter Commutation Strategies With and Without Explicit Input Voltage Sign Measurement,” IEEE Trans. on Industrial Electronics, Vol.49, No.2, pp.407-414, 2002
[14] C. Piao and J. Y. Hung, "Analysis and compensation of dead-time effect in direct matrix converter," 2015 IEEE Conference on Technologies for Sustainability (SusTech), Ogden, UT, 2015, pp. 90-95.
[15] R. M. Cuzner, A. R. Bendre, P. J. Faill and B. Semenov, "Implementation of a Four-Pole Dead-Time-Compensated Neutral-Point-Clamped Three-Phase Inverter With Low Common-Mode Voltage Output," in IEEE Transactions on Industry Applications, vol. 45, no. 2, pp. 816-826, March-april 2009.
[16] M. Sprenger, R. Alvarez and S. Bernet, "Direct dead-time control - a novel DC-link neutral-point balancing method for the three-level neutral-point-clamped voltage source inverter," 2012 IEEE Energy Conversion Congress and Exposition (ECCE), Raleigh, NC, 2012, pp. 1157-1163.
[17] X. Zhang, D. Boroyevich, R. Burgos, P. Mattavelli and F. Wang, "Impact and compensation of dead time on common mode voltage elimination modulation for neutral-point-clamped three-phase inverters," 2013 IEEE ECCE Asia Downunder, Melbourne, VIC, 2013, pp. 1016-1022.
[18] J. Zhang, L. Li, D. Dorrell and Y. Guo, "A PI controller with current feedforward to improve the steady-state error performance for a current controlled direct matrix converter," 2017 20th International Conference on Electrical Machines and Systems (ICEMS), Sydney, NSW, 2017, pp. 1-6.
[19] J. Zhang, L. Li, and D. Dorrell, "DQ Coupling Suppressed PID Controller for the Transmission Line Power Flow Control Using a Matrix Converter," IEEE Ind. Electron. Soc. Annu. Meeting (IECON16), Florence, Italy, pp. 6249 –6254, October 2016.
[20] J. Zhang, D. Dorrell, and L. Li, "Applications of the Direct Space Vector Modulation Controlled Matrix Converter as the Unified Power Flow Controller," 8th Int. conf. power electron. motor drives (PEMD206), Glasgow, UK, pp. 1-6, April 2016.
[21] K. Ogata, "PID controllers and modified PID controllers," in Modern Control Engineering, fifth edition, EARSON, pp. 577-651, 2010.
[22] H. Takahashi and J. i. Itoh, "Ride through capability of matrix converter for grid connected system under short voltage sag," IECON 2015 - 41st Annual Conference of the IEEE Industrial Electronics Society, Yokohama, 2015, pp. 005298-005303.
[23] P. Nielsen, F. Blaabjerg and J. K. Pedersen, "New protection issues of a matrix converter: design considerations for adjustable-speed drives," in IEEE Transactions on Industry Applications, vol. 35, no. 5, pp. 1150-1161, Sep/Oct 1999.
[24] C. Klumpner, P. Nielsen, I. Boldea and F. Blaabjerg, "A new matrix converter motor (MCM) for industry applications," in IEEE Transactions on Industrial Electronics, vol. 49, no. 2, pp. 325-335, Apr 2002.