本論文之研究主題是設計消除漣波之諧波電流注入方程式，降低漣波污染電壓穩定性和避免諧波相互干擾。邇來，多階層模組轉換器為具可拓展性高功率應用的拓撲結構之一，其廣泛應用在高壓併網、直流傳輸、電力轉換系統，以及儲能設備場和再生能源發電站。現今，再生能源系統作為刺激能源轉換和減少溫室氣體排放的動力來源，已擘畫出綠色能源之發展藍圖。然而，現有的控制法則，無法精確地揭露出多階層模組轉換器固有特性。基於上述理由，本研究結合直接數位控制法所推導出之模組電壓數學表示式及能源相關成本函數中拉格朗日乘數演算法，用以分析漣波貢獻度，針對其漣波成分釐清振幅、頻率及角度變動量，據以設計出消除漣波之諧波電流注入方程式。在此設計法則下，找出一個可降低漣波影響之最佳注入策略，平衡諧波污染及傳導損失對系統穩定性之貢獻。
總而言之，本論文之主要貢獻概述如下：驗證了一個基於零平均電流注入法則，具有降低漣波影響系統電力品質之可行性。同時，提出了一個基於零平均電流控制命令最佳化，以確保多階層模組電壓漣波，上下臂電流擺動以及系統環流抑制之平衡策略。此外，本論文提出消除漣波之諧波電流注入模型，可以為間歇性電源智慧併網、消除諧波污染以及電驛保護協調的研究提供重要基礎。
本研究所提出的設計、控制和穩定度分析方法，已經由MATLAB Simulink的模擬和採用模組化多階層架構3 kW轉換器測試平台的實驗結果得到驗證。另外，此平台主要驗證我們所提出控制法的可行性，以測試模組電壓表示式、直接數位控制法則、降低模組電壓漣波與平衡模組電壓及環流抑制之影響。由於分析與實驗結果的吻合度，驗證在不同零平均電流組合注入法下有效抑制漣波的適用性。

關鍵字:直接數位控制法則、模組電壓漣波抑制、模組化多階層架構、拉格朗日最佳化、零平均電流控制命令注入法

This dissertation presents unique approaches to deriving cell-voltage expression in terms of arm currents, injected zero-mean current and duty-ratio control laws, on which cell-voltage ripple reduction and arm-current swing suppression can be achieved. Currently, Modular Multilevel Converter (MMC) is one of the most possible topologies for high power applications with scalability, which has been widely applied to high-voltage grid power injection, direct-current transmission, power transfer systems, energy storage yards and renewable energy generation stations. Nowadays, the renewable energy system is especially the source of momentum which stimulates energy transition and reduction of greenhouse gas emissions. However, its existing control schemes may not precisely reveal the inherent mannerism of MMCs.
This study is to optimize the cell voltage, arm current and circulating current of converter arms in MMC based on Lagrange multiplier of energy cost function and arm current tracking control law. Meanwhile, determination of the parameters of magnitude, frequency, and phase are due to the contribution analysis of the proposed cell-voltage ripple expression, and a harmonic current injection function in terms of this design method is proposed to reduce ripple influences on the power quality of MMC.
To sum up, the major contributions are summarized as follows: the practicality of the proposed methodology is demonstrated through a scene study and the unique ap-proach based on zero-mean current injection principle is also proposed to suppress the ripple effect under different current injection combinations. Meanwhile, a trade-off strategy among cell voltage, arm current swing and circulating current is proposed to select the optimal zero-mean current command injection combinations. Moreover, this article paved the way for a new research cornerstone of smart grid interconnection, eliminating harmonic pollutions, and relay coordination.
Simulated and experimental results from a 3 kW single-phase MMC have verified the functionality of the proposed control method, analysis and comprehensive discus-sion. The practicality of the proposed design method has been verified for different design scenarios in terms of the proposed cell-voltage expression, direct digital control, cell-voltage ripple reduction and trade-off cell-voltage and circulating current. Moreover, the analytical results have also been revealed to be in good accordance with experimental results, which confirms the applicability of injected effectiveness in ripple suppression analysis methods under different ZMCCI combinations.

Keywords: Direct digital control algorithm, Cell-voltage ripple reduction, MMC, La-grange optimization, Zero-mean current command injection

[1] United Nations, "The Pair Agreement", UNFCCC COP21, Dec. 2015.
[2] Taipower Sustainability (2018, Dec. 31). Stable power supply. retrieved from https://csr.taipower.com.tw/en/sitemap.aspx.
[3] Z. Shu, M. Liu, L. Zhao, S. Song, Q. Zhou, and X. He, “Predictive Harmonic Control and Its Optimal Digital Implementation for MMC-Based Active Power Filter”, IEEE Trans. Industrial Electron., vol. 63, no. 8, pp. 5244-5254, Aug. 2016.
[4] X. Xie, “Control Strategy of Active Power Filter Based on Modular Multilevel Con-verter”, IOP Conference Series: Materials Science and Engineering, Volume 322, Issue 7, pp. 072032, Mar. 2018.
[5] F. T. Ghetti, A. A. Ferreira, H. A. C. Braga and P. G. Barbosa, "A study of shunt ac-tive power filter based on modular multilevel converter (MMC)," 2012 10th IEEE/IAS International Conference on Industry Applications, Fortaleza, pp. 1-6, 2012.
[6] M. S. Hamad, K. H. Ahmed and A. I. Madi, "Current harmonics mitigation using a modular multilevel converter-based shunt active power filter," 2016 IEEE Interna-tional Conference on Renewable Energy Research and Applications (ICRERA), Bir-mingham, pp. 755-759, Nov. 2016.
[7] C. Li, K. Dai, D. Lin, C. Xu, C. Chen, and Z. Dai, “Independent positive- and nega-tive-sequence control for MMC-SAPF with unbalanced PCC voltage”, ECCE2017 Cincinnati, USA, pp. 1823-1829, Oct. 2017.
[8] T. Isobe, L. Zhang, et al., “Experimental verification of capacitance reduction in MMC-based STATCOM”, IEEE ECCE2016 USA, ISBN: 978-1-5090-0738-7, pp. 1-7, 2016.
[9] G. Tsolaridis, E. Kontos, H. Parikh, R. M. S.-Loeches, R. Teodorescu, and S. K. Chaudhary,“Control of a Modular Multilevel Converter STATCOM under internal and external unbalances”, IEEE IECON2016 Italy, pp. 6494-6499, Oct. 2016.
[10] C. Allan, F. João, P. Heverton, J. S.I., T. Remus, “DSCC-MMC STATCOM Main Circuit Parameters Design Considering Positive and Negative Sequence Compensa-tion”, Journal of Control, Automation and Electrical Systems, vol. 29, no. 1, pp. 62–74, Feb. 2018.
[11] J. Mei, B. Xiao, K. Shen, L. M. Tolbert and J. Y. Zheng, "Modular Multilevel Invert-er with New Modulation Method and Its Application to Photovoltaic Grid-Connected Generator," in IEEE Transactions on Power Electron., vol. 28, no. 11, pp. 5063-5073, Nov. 2013.
[12] V. S. Prasadarao K, P. S. Rani and G. Tabita, "A new multi-level inverter topology for grid interconnection of PV systems," 2014 POWER AND ENERGY SYSTEMS: TOWARDS SUSTAINABLE ENERGY, Bangalore, pp. 1-5, 2014.
[13] A. E. Leon, and S. J. Amodeo, “Energy Balancing Improvement of Modular Multi-level Converters Under Unbalanced Grid Conditions”, in IEEE Transactions on Power Electron., vol. 32, no. 8, pp. 6628–6637, Aug. 2017.
[14] X. Shi, Z. Wang, B. Liu, Y. Li, L. M. Tolbert, and F. Wang, “Steady-State Modeling of Modular Multilevel Converter Under Unbalanced Grid Conditions”, in IEEE Transactions on Power Electron., vol. 32, no. 9, pp. 7306–7324, Sep. 2017.
[15] M. Singh, V. Khadkikar, A. Chandra and R. K. Varma, "Grid Interconnection of Re-newable Energy Sources at the Distribution Level with Power-Quality Improvement Features," in IEEE Transactions on Power Delivery, vol. 26, no. 1, pp. 307-315, Jan. 2011.
[16] T. Nakanish, K. Orikawa, and J.-I. Itoh, “Modular Multilevel Converter for wind power generation system connected to micro-grid”, 2014 ICRERA Milwaukee, USA, pp. 653–658, Oct. 2014.
[17] Z. Huibin, J. Dragan, Y. Liangzhong, X. Wang, W. Jinyu, “Transmission level MMC DC/DC Converter for large scale integration of renewable energy into HVDC grid,” IPEMC 2016 – ECCE Asia, pp. 2602-2608, May. 2016.
[18] Z. Lei, Z. Zhang, J. Qin, D. Shi, Z. Wang, “Design and Performance Evaluation of the Modular Multilevel Converter (MMC)-based Grid-tied PV-Battery Conversion System.” 2018 IEEE Energy Conversion Congress and Exposition, pp. 2649-2654, Dec. 2018.
[19] S. Cui, S. Kim, J.-J. Jung, and S.-K. Sul, “A comprehensive cell capacitor energy control strategy of a modular multilevel converter (MMC) without a stiff DC bus voltage source” IEEE-APEC2014. USA, pp. 602–609, Mar. 2014.
[20] S. Samimi, F. Gruson, X. Guillaud and P. Delarue, "Control of DC bus voltage with a Modular Multilevel Converter," 2015 IEEE Eindhoven PowerTech, Eindhoven, pp. 1-6, 2015.
[21] S. Samimi, F. Gruson, P. Delarue, F. Colas, M. M. Belhaouane, and X. Guillaud, “MMC Stored Energy Participation to the DC Bus Voltage Control in an HVDC Link.”, in IEEE Transactions on Power Delivery, pp.1710-1718, 2016.
[22] Z. Ou, G. Wang and J. Feng, "Two control strategies of modular multilevel converter in rectifier side based on arm current under unbalanced voltage condition," 2015 5th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies (DRPT), Changsha, pp. 2281-2286, Nov. 2015.
[23] Y. Liang, J. Liu, T. Zhang and Q. Yang, "Arm Current Control Strategy for MMC-HVDC Under Unbalanced Conditions," in IEEE Transactions on Power De-livery, vol. 32, no. 1, pp. 125-134, Feb. 2017.
[24] L. Danqing, W. Guangzhu, O. Zhujian and L. Jiaxing, "A Control Strategy of MMC Battery Energy Storage System Based on Arm Current Control," 2018 International Power Electronics Conference (IPEC-Niigata 2018 -ECCE Asia), pp. 1376-1380, 2018.
[25] Z. Ou, G. Wang, and L. Zhang, “Modular Multilevel Converter Control Strategy Based on Arm Current Control Under Unbalanced Grid Condition”, in IEEE Trans-actions on Power Electron., Vol. 33, no. 5, pp. 3826-3836, May 2018.
[26] H. A. Pereira, M. R. Haddioui, L. O. M. de Oliveira, L. Mathe, M. Bongiorno and R. Teodorescu, "Circulating current suppression strategies for D-STATCOM based on modular multilevel converters," 2015 IEEE 13th Brazilian Power Electronics Con-ference and 1st Southern Power Electronics Conference (COBEP/SPEC), Fortaleza, pp. 1-6, 2015.
[27] Y. Ma and L. Fan, "Circulating current and DC current ripple control in MMC under unbalanced grid voltage," 2015 North American Power Symposium (NAPS), Char-lotte, NC, pp. 1-6, 2015.
[28] J. Wang, J. Liang, C. Wang, and X. Dong, “Circulating current suppression for MMC-HVDC under unbalanced grid conditions” in IEEE Industry Applications So-ciety Annual Meeting, pp. 1-9, 2016.
[29] B. Bahrani, S. Debnath and M. Saeedifard, "Circulating Current Suppression of the Modular Multilevel Converter in a Double-Frequency Rotating Reference Frame," in IEEE Transactions on Power Electron., vol. 31, no. 1, pp. 783-792, Jan. 2016.
[30] G. Qiang, Y. Xi and L. Ye, "Circulating Current Suppressing and AC Faults Ride-Through Capability Analysis of Zhoushan MMC-MTDC System," 2018 2nd IEEE Conference on Energy Internet and Energy System Integration (EI2), Beijing, pp. 1-6, 2018.
[31] S. Yang, P. Wang, Y. Tang, M. Zagrodnik, X. Hu and K. J. Tseng, “Circulating Cur-rent Suppression in Modular Multilevel Converters with Even-Harmonic Repetitive Control”, in IEEE Trans. on Industry Applications, vol. 54, no. 1, pp. 298-309, Feb. 2018.
[32] Y. Xu, Z. Xu, Z. Zhang and H. Xiao, "A Novel Circulating Current Controller for MMC Capacitor Voltage Fluctuation Suppression," in IEEE Access, vol. 7, pp. 120141-120151, 2019.
[33] J. Jung, H. Lee and S. Sul, "Control Strategy for Improved Dynamic Performance of Variable-Speed Drives with Modular Multilevel Converter," in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 3, no. 2, pp. 371-380, June 2015.
[34] J. Wang, R. Burgos and D. Boroyevich, "Model-Predictive Control to realize the Switching-Cycle Capacitor Voltage Control for the modular multilevel converters," 2015 IEEE Applied Power Electronics Conference and Exposition (APEC), Charlotte, NC, pp. 1512-1519, 2015.
[35] T.-F. Wu, C.-W. Huang, T.-C. Chou, and K. Sun, "Cell-Voltage Ripple Reduction for Modular Multilevel Converters with Zero-Mean Current Command Injection," 2018 IEEE International Power Electronics and Application Conference and Exposition (PEAC), Shenzhen, pp. 1-6, 2018.
[36] M. Hagiwara, R. Maeda, and H. Akagi, “Control and analysis of the modular multi-level cascade converter based on double-star chopper-cells (MMCC-DSCC)”, in IEEE Transactions on Power Electron., Vol. 26, no. 6, pp. 1649-1658, Jun. 2011.
[37] S. Hamasaki, K. Hadano, S. Eguchi and M. Tsuji, "Control of full bridge type modular multilevel converter for single phase AC/AC conversion," 2016 19th International Conference on Electrical Machines and Systems (ICEMS), Chiba, pp. 1-6, 2016.
[38] A. Lashab, D. Sera, J. Martins and J. M. Guerrero, "Multilevel DC-Link Convert-er-Based Photovoltaic System with Integrated Energy Storage," 2018 5th Interna-tional Symposium on Environment-Friendly Energies and Applications (EFEA), Rome, pp. 1-6, 2018.
[39] R. Picas, J. Pou, S. Ceballos, V. G. Agelidis, and M. Saeedifard, “Minimization of the capacitor voltage fluctuations of a modularmultilevel converter by circulating current control”, in Froc. iEEE industrial Electronics Conference (iECON'12) Mon-treal, Canada, Oct. 2012.
[40] J. Moon, C. Kim, J. Park, D. Kang and J. Kim, "Circulating Current Control in MMC Under the Unbalanced Voltage," in IEEE Transactions on Power Delivery, vol. 28, no. 3, pp. 1952-1959, July 2013.
[41] A. U. Lawan, H. A. F. Almurib, J. G. Khor and S. Babani, "Circulating Current con-trol of a Modular Multilevel Converter (MMC) with State Feedback Controller and Harmonic Current Suppression," 2018 IEEE International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles & International Transportation Electrification Conference (ESARS-ITEC), Nottingham, pp. 1-8, 2018.
[42] R. Marquardt and A. Lesnicar, “A new modular voltage source inverter topology,” in Proc. of Rec. Eur. Conf. Power Electr. Appl., France, 2003.
[43] H. Akagi, "Classification, terminology, and application of the modular multilevel cascade converter (MMCC)," in IEEE Transactions on Power Electron., vol. 26, no. 11, pp. 3119-3130, Nov. 2011.
[44] S. Kannan, C. Poongothai, I. Colak and W. Ali, "Selective Harmonic Elimination for Modular Multilevel Converter with Averaging and Circulating Current Control," 2018 7th International Conference on Renewable Energy Research and Applications (ICRERA), Paris, pp. 221-226, 2018.
[45] R. Picas, J. Pou, S. Ceballos, J. Zaragoza, G. Konstantinou, and V. G. Agelidis, “Op-timal injection of harmonics in circulating currents of modular multilevel converters for capacitor voltage ripple minimization,” in Proc. ECCE Asia Downunder (ECCE Asia), Melbourne, pp. 318-324, Australia, Jun. 2013.
[46] J. Pou, S. Ceballos, G. Konstantinou, V. G. Agelidis, R. Picas, and J. Zaragoza, “Circulating current injection methods based on instantaneous information for the MMC”, in IEEE Trans. Ind. Electron., vol. 62, pp. 777-788, Feb. 2014.
[47] L. Yang, Y. Li, Z. Li, P. Wang, S. Xu and R. Gou, "Loss Optimization of MMC by Second-Order Harmonic Circulating Current Injection," in IEEE Transactions on Power Electron., vol. 33, no. 7, pp. 5739-5753, July 2018.
[48] H. Jiang, L. Xiao and C. Wang, "Adaptive loss and capacitance-reduction control strategy based on second-harmonic circulating current injection for MMC," in IET Power Electronics, vol. 12, no. 11, pp. 2821-2831, 2019.
[49] X. Wang., T. AN., J. Yang and C. Zhao., "Conditions on Optimum Percentage of Second-order Harmonic Circulating Current Injection Based on MMC," 2019 IEEE 3rd Information Technology, Networking, Electronic and Automation Control Con-ference (ITNEC), Chengdu, China, pp. 976-981, 2019.
[50] Q. Tu, Z. Xu, and L. Xu, “Reduced-switching frequency modulation and circulating current suppression for modular multilevel converters,” in IEEE Transactions Power Delivery, vol. 26, no. 3, pp. 2009-2017, July 2011.
[51] G. A. Reddy and A. Shukla, "Circulating Current Elimination Controller for Modular Multilevel Converter and Submodule Capacitor Voltage Analysis," 2018 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), Chennai, India, pp. 1-6, 2018.
[52] T.-F. Wu, C.-W. Huang, T.-C. Chou, J.-S. Chen and Y. Chang, “Investigation of cell voltages and arm currents in double-star modular multilevel converters”, IFEEC 2017-ECCE Asia, pp. 539-544, Jun. 2017.
[53] G. Bergna et al., "A Generalized Power Control Approach in ABC Frame for Modu-lar Multilevel Converter HVDC Links Based on Mathematical Optimization," in IEEE Transactions on Power Delivery, vol. 29, no. 1, pp. 386-394, Feb. 2014.
[54] X. Xifeng et al., "Research on model predictive control for modular multilevel con-verter," 2017 IEEE 2nd Information Technology, Networking, Electronic and Auto-mation Control Conference (ITNEC), Chengdu, pp. 272-276, 2017.
[55] T.-F. Wu, C.-W. Huang, T.-C. Chou, “Lagrange-Based Optimization of Cell Voltage and Arm Current with Zero-Sequence Current Injection in Modular Multilevel Con-verter”, ECCE2017 Cincinnati, USA, pp.4538-4545, Oct. 2017.
[56] G. Bergna et al., "Improving the dynamics of lagrange-based MMC controllers by means of adaptive filters for single-phase voltage, power and energy estimation," IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society, Vienna, pp. 6239-6244, 2013.
[57] G. Bergna, J. A. Suul, E. Berne, et al., “MMC circulating current reference calcula-tion in ABC frame by means of Lagrange Multipliers for ensuring constant DC power under unbalanced grid conditions”, Power Electronics and Applications (EPE'14-ECCE Europe), 2014 16th European, pp. 1-10, 2014.
[58] R. Khatami, M. Parvania and P. P. Khargonekar, "Scheduling and Pricing of Energy Generation and Storage in Power Systems," in IEEE Transactions on Power Systems, vol. 33, no. 4, pp. 4308-4322, July 2018.
[59] C. Li, Y. Lyu and F. C. Lee, "State trajectory analysis for modular multilevel con-verter," 2016 IEEE International Power Electronics and Motion Control Conference (PEMC), Varna, pp. 482-491, 2016.
[60] Y. Lyu, C. Li, Y. Hsieh, F. C. Lee, Q. Li and R. Xu, “Capacitor Voltage Ripple Re-duction with State Trajectory Analysis for Modular Multilevel Converter” 2017 IEEE Applied Power Electronics Conference and Exposition (APEC), Tampa, FL, pp. 1829-1836, 2017.
[61] Y. Hsieh and F. C. Lee, "Decoupled αβ model of modular multilevel converter (MMC)," 2017 IEEE Energy Conversion Congress and Exposition (ECCE), Cincin-nati, OH, pp. 1521-1526, 2017.
[62] X. Liu, D. Wang, G. Guo, et al., “The multi-level simplified simulation of MMC based on half-bridge sub-models”, Chinese Control Conference, pp. 9935-9941, 2016.
[63] F. Hohmann and M. Bakran, "Improved performance for half bridge cells with parallel press-pack diode," 2017 IEEE 12th International Conference on Power Electronics and Drive Systems (PEDS), Honolulu, HI, pp. 75-80, 2017.
[64] D. Vozikis, G. Adams, P. Rault, O. Despouys, D. Holliday and S. Finney, "Enhanced Multilevel Modular Converter with Reduced Number of Cells and Harmonic Con-tent," in IEEE Journal of Emerging and Selected Topics in Power Electronics, Mar 2019.
[65] T.-F. Wu, L. Lin, N. Yao, Y. Chen and Y. Chang, "Extended Application of D- Σ Dig-ital Control to a Single-Phase Bidirectional Inverter with an LCL Filter," in IEEE Transactions on Power Electron., vol. 30, no. 7, pp. 3903-3911, July 2015.
[66] T.-F. Wu, T.-C. Chou, Z.-C. Guo, C.-S. Wu and C.-W. Huang, "D-Σ digital control based modular multilevel converter," 2016 IEEE 8th International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia), Hefei, pp. 3501-3507, 2016.
[67] M. Zhang, L. Huang, W. Yao and Z. Lu, "Circulating Harmonic Current Elimination of a CPS-PWM-Based Modular Multilevel Converter with a Plug-In Repetitive Controller," in IEEE Transactions on Power Electron., vol. 29, no. 4, pp. 2083-2097, April 2014.
[68] L. Yang, Y. Li, Z. Li, P. Wang, S. Xu, R. Gou,” Loss Optimization of MMC by Sec-ond-Order Harmonic Circulating Current Injection.” in IEEE Transactions on Power Electron., vol. 33, no. 7, pp. 5739-5753, July 2018.
[69] Cree Inc., Silicon Carbide Power MOSFET C2M TM MOSFET Technology - C2M0025120D Datasheet, Oct 2015, Rev. B.
[70] IEEE Std 519TM-2014. IEEE Recommended Practice and Requirements for Harmon-ic Control in Electric Power Sys¬tems. IEEE Power and Energy Society. 2014. 1-29.
[71] T. Hoevenaars, K. LeDoux and M. Colosino, "Interpreting IEEE STD 519 and meet-ing its harmonic limits in VFD applications," IEEE Industry Applications Society 50th Annual Petroleum and Chemical Industry Conference, 2003, Houston, TX, USA, pp. 145-150, 2003.
[72] T. Amir, A. Ahmad, M. E. Adabi, etc, "A Fault-Tolerant Control Strategy of Modular Multilevel Converter with Sub-Module Faults Based on Neutral Point Compound Shift," An Asymmetrical Step-Up Multilevel Inverter Based on Switched-Capacitor Network," Sustainability, MDPI, Open Access Journal, vol. 11, no. 7, pp. 1-18, June 2019.
[73] Q. Zhu, W. Dai, L. Guan, X. Tan, Z. Li, and D. Xie, "A Fault-Tolerant Control Strat-egy of Modular Multilevel Converter with Sub-Module Faults Based on Neutral Point Compound Shift," Energies. 12. 876, 2019.