本論文提出一種三相四線式混頻並聯換流器系統的分析與設計，解決高功率換流器在高切換頻率下的運作限制。在避免使用高價高頻高功率開關元件情況下，提升系統動態響應、保有低頻漣波抑制功能、以及降低輸出濾波器體積。本研究透過時域數學模型，設計混頻電壓電流控制演算法，也透過時域與頻域設計低頻漣波抑制演算法，並分析系統穩定度，達成混頻並聯換流器的濾波器設計。
在高功率混頻換流器與單、雙台並聯換流器的比較方面，本研究透過供應商提供的開關與鐵芯參數建立MATLAB Simulink開關切換損失、開關導通損失、鐵芯切換損失、導線導通損失等數學模型，並透過dc 760 V/ac 380 V/300 kVA規格，來模擬混頻與單、雙台並聯換流器的性能。結合比較不同頻率單/雙台並聯換流器中的電壓/電流總諧波失真率、暫態響應、電感體積、開關元件成本以及系統效率，本研究根據各式性能指標，指出混頻並聯換流器相較於單/雙台低頻轉換器具有動態提升、抑制電壓電流總諧波失真率以及縮小濾波器體積之效果，同時相較於單/雙高頻轉換器具有損耗抑制以及成本控制之效果，驗證高頻轉換器之應用場域與定位。
在系統功能驗證方面，受限於環境容量，本研究透過建造一台dc 760 V/ac 380 V/10 kVA的三相四線式混頻換流器，並實際測試來驗證併網型與不斷電系統型功能。同時為了驗證MATLAB Simulink模擬模型的有效性，本研究比對dc 760 V/ac 380 V/10 kVA的三相四線式混頻換流器實測驗證結果與同規格下的MATLAB Simulink模擬結果，驗證Simulink模型與實測結果的一致性，也間接提升dc 760 V/ac 380 V/300 kVA規格模擬的有效性。
透過模擬與實測結果，本論文驗證混頻並聯換流器系統，具有提升系統動態響應、保有低頻漣波抑制以及降低輸出濾波器體積之功能。混頻並聯換流器系統可於併網型應用中提高電流追蹤表現，符合IEEE-519之電流注入電網規範。同時，混頻並聯換流器系統可於不斷電系統應用中提升電壓追蹤表現，提供線性負載、整流性負載以及瞬間加載所需的穩定電壓，滿足IEC 62040-3的穩壓規範。
本研究的原創性貢獻簡述如下：
混頻並聯換流器成功整合低頻高功率與高頻低功率換流器，提供系統足夠的動態響應，且避免使用高單價的高頻高功率元件，節省開關成本，增加開關的選擇性。
混頻並聯換流器透過低頻高功率開關元件和高頻低功率開關元件達到不對稱分流，增加系統頻率與功率設計上的自由度，提供相關應用對所需性能規格與成本規格上的平衡選擇。
混頻並聯換流器在不同開關切換頻率下仍然具有低頻漣波抑制功能，使輸出只有高頻漣波成分，有效縮小並聯換流器所需的輸出濾波器體積。
提出混頻並聯換流器的濾波器設計方法與穩定度分析，確保混頻並聯換流器在不同規格下的穩定運行。
提出混頻並聯換流器電流與電壓控制演算法結合漣波抑制演算法與濾波器設計，有效確保輸出電壓電流總諧波失真率與暫態響應符合IEEE-519與IEC 62040-3系統規範。

In this dissertation, a hybrid frequency parallel inverter system (HbFPIS) is presented as a parallel-inverter solution to provide sufficient dynamic performance improvements, current/voltage tracking performance, freedom of designing power/frequency, filter-volume reduction, cost reduction, and loss reduction for power conversion in grid-connected (GC), active power filter (APF), and uninterruptible power supply (UPS) applications. The control algorithm, system parameter design, piece-wise linear model, and stability analyses of the HbFPIS are derived and analyzed with time-domain and frequency-domain models, providing a complete view and design process for future applications.
Based on the comparisons among the simulated results of the 300 kVA single and parallel inverters with different switching frequencies, the proposed HbFPIS has the compromise current/voltage regulation performances between low-frequency (LF) and high-frequency (HF) parallel inverters. The voltage/current total harmonic distortions and filter volume of HbFPIS are lower than those of the LF inverters. The switch cost and loss of HbFPIS are lower than those of HF inverters. The sufficient current/voltage regulation performances are achieved without over-designed high-cost switches applied in single/parallel HF inverters. This indicates that the HbFPIS is a third option that avoids extreme solutions with either low or over-designed performances, costs and losses.
Finally, with the derived controls, designed system parameters, piece-wise linear models, and linear stability analysis, the simulated and experimental results of the designed 10 kVA HbFPIS validate the current/voltage tracking functions, ripple compensation, distortion reduction, dynamic improvement, steady-state system stability, and transient system stability. The output current total harmonic distortions (THDs) complying with the IEEE-519 standard and the output voltage THDs and errors complying with IEC 62040-3 standard indicate that the HbFPIS is a feasible solution for GC, APF and UPS applications.
The original contribution of the dissertation includes the following items:
The proposed HbFPIS successfully combines high-power LF and low-power HF inverters. The integration provides sufficient dynamic response without over-designed high-power HF switches with extra cost. This reduces the construction cost of the inverter and increases the selection of available switches.
The proposed HbFPIS can achieve unbalanced current sharing with switches designed for different frequencies and power ratings. This provides higher design freedom and possibility to balance the performance and cost.
The ripple compensation function of the HbFPIS allows LF ripple attenuation with non-identical switching frequencies. This results in filter-volume reduction for the only remaining HF ripples in output current/voltages.
The filter and system parameter design can ensure the functionality and system stability of the HbFPIS with different power ratings and switching frequencies.
The derived controls, ripple compensation algorithm, and filter design ensure the current/voltage THDs and dynamic performances complying with IEEE-519 and IEC 62040-3.

[1] IRENA (2020), Renewable Energy Statistics 2020. The International Renewable Energy Agency, Abu Dhabi. ISBN 978-92-9260-246-8.
[2] IEA (2019), Global Energy & CO2 Status Report. The latest trends in energy and emissions in 2018. International Energy Agency Publications, France.
[3] IEA (2021). Global Energy Review 2021. Assessing the effects of economic recoveries on global energy demand and CO2 emissions in 2021. International Energy Agency Publications, France.
[4] S. O. Muhanji, A. Muzhikyan and A. M. Farid, "Distributed Control for Distributed Energy Resources: Long-Term Challenges and Lessons Learned," IEEE Access, vol. 6, pp. 32737-32753, 2018
[5] A. Bidram, F. L. Lewis and A. Davoudi, "Distributed Control Systems for Small-Scale Power Networks: Using Multiagent Cooperative Control Theory," IEEE Control Systems Magazine, vol. 34, no. 6, pp. 56-77, Dec. 2014.
[6] F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus, "Overview of Control and Grid Synchronization for Distributed Power Generation Systems," IEEE Transactions on Industrial Electronics, vol. 53, no. 5, pp. 1398-1409, Oct. 2006.
[7] R. H. Lasseter et al., "CERTS Microgrid Laboratory Test Bed," IEEE Transactions on Power Delivery, vol. 26, no. 1, pp. 325-332, Jan. 2011.
[8] P. Wang, L. Goel, X. Liu, and F. H. Choo, "Harmonizing AC and DC: A Hybrid AC/DC Future Grid Solution," IEEE Power and Energy Magazine, vol. 11, no. 3, pp. 76-83, May-Jun. 2013.
[9] S. Abu-Elzait and R. Parkin, "Economic and Environmental Advantages of Renewable-based Microgrids over Conventional Microgrids," 2019 IEEE Green Technologies Conference(GreenTech), 2019, pp. 1-4.
[10] P. C. Loh, D. Li, Y. K. Chai, and F. Blaabjerg, "Autonomous Operation of Hybrid Microgrid With AC and DC Subgrids," IEEE Transactions on Power Electronics, vol. 28, no. 5, pp. 2214-2223, May 2013.
[11] P. C. Loh, D. Li, Y. K. Chai, and F. Blaabjerg, "Hybrid AC–DC Microgrids With Energy Storages and Progressive Energy Flow Tuning," IEEE Transactions on Power Electronics, vol. 28, no. 4, pp. 1533-1543, Apr. 2013.
[12] D. E. Olivares et al., "Trends in Microgrid Control," IEEE Transactions on Smart Grid, vol. 5, no. 4, pp. 1905-1919, Jul. 2014.
[13] N. Hatziargyriou, H. Asano, R. Iravani, and C. Marnay, "Microgrids," IEEE Power and Energy Magazine, vol. 5, no. 4, pp. 78-94, Jul.-Aug. 2007.
[14] M. Morati, D. Girod, F. Terrien, V. Peron, P. Poure, and S. Saadate, "Industrial 100-MVA EAF Voltage Flicker Mitigation Using VSC-Based STATCOM With Improved Performance," IEEE Transactions on Power Delivery, vol. 31, no. 6, pp. 2494-2501, Dec. 2016.
[15] M. Hagiwara, R. Maeda and H. Akagi, "Negative-Sequence Reactive-Power Control by a PWM STATCOM Based on a Modular Multilevel Cascade Converter (MMCC-SDBC)," IEEE Transactions on Industry Applications, vol. 48, no. 2, pp. 720-729, Mar.-Apr. 2012.
[16] K. Hu and C. Liaw, "Incorporated Operation Control of DC Microgrid and Electric Vehicle," IEEE Transactions on Industrial Electronics, vol. 63, no. 1, pp. 202-215, Jan. 2016.
[17] S. Lin et al., "Research on the Regeneration Braking Energy Feedback System of Urban Rail Transit," IEEE Transactions on Vehicular Technology, vol. 68, no. 8, pp. 7329-7339, Aug. 2019.
[18] M. Khodaparastan, A. A. Mohamed, and W. Brandauer, “Recuperation of regenerative braking energy in electric rail transit systems,” IEEE Trans. Intell. Transp. Syst., vol. 20, no. 8, pp. 2831–2847, Aug. 2019.
[19] M. Aamir and S. Mekhilef, "An Online Transformerless Uninterruptible Power Supply (UPS) System with a Smaller Battery Bank for Low-Power Applications," IEEE Transactions on Power Electronics, vol. 32, no. 1, pp. 233-247, Jan. 2017.
[20] C. G. C. Branco, R. P. Torrico-Bascope, C. M. T. Cruz, and F. K. de A. Lima, "Proposal of Three-Phase High-Frequency Transformer Isolation UPS Topologies for Distributed Generation Applications," IEEE Transactions on Industrial Electronics, vol. 60, no. 4, pp. 1520-1531, Apr. 2013.
[21] E. Kim, F. Mwasilu, H. H. Choi, and J. Jung, "An Observer-Based Optimal Voltage Control Scheme for Three-Phase UPS Systems," IEEE Transactions on Industrial Electronics, vol. 62, no. 4, pp. 2073-2081, Apr. 2015.
[22] L. Asiminoaei, E. Aeloiza, P. N. Enjeti, and F. Blaabjerg, "Shunt Active-Power-Filter Topology Based on Parallel Interleaved Inverters," IEEE Transactions on Industrial Electronics, vol. 55, no. 3, pp. 1175-1189, Mar. 2008.
[23] J. Chen, D. Sha, J. Zhang, and X. Liao, "A Variable Switching Frequency Space Vector Modulation Technique for Zero-Voltage Switching in Two Parallel Interleaved Three-Phase Inverters," IEEE Transactions on Power Electronics, vol. 34, no. 7, pp. 6388-6398, Jul. 2019.
[24] A. Zorig, S. Barkat, M. Belkheiri, A. Rabhi, and F. Blaabjerg, "Novel Differential Current Control Strategy Based on a Modified Three-Level SVPWM for Two Parallel-Connected Inverters," IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 5, no. 4, pp. 1807-1818, Dec. 2017.
[25] Y. Xia, M. Yu, Y. Peng, and W. Wei, "Modeling and Analysis of Circulating Currents Among Input-Parallel Output-Parallel Nonisolated Converters," IEEE Transactions on Power Electronics, vol. 33, no. 10, pp. 8412-8426, Oct. 2018.
[26] F. Wang, Y. Wang, Q. Gao, C. Wang, and Y. Liu, "A Control Strategy for Suppressing Circulating Currents in Parallel-Connected PMSM Drives with Individual DC Links," IEEE Transactions on Power Electronics, vol. 31, no. 2, pp. 1680-1691, Feb. 2016.
[27] Z. Xueguang, W. Li, Y. Xiao, G. Wang, and D. Xu, "Analysis and Suppression of Circulating Current Caused by Carrier Phase Difference in Parallel Voltage Source Inverters With SVPWM," IEEE Transactions on Power Electronics, vol. 33, no. 12, pp. 11007-11020, Dec. 2018.
[28] X. Zhang, T. Wang, X. Wang, G. Wang, Z. Chen, and D. Xu, "A Coordinate Control Strategy for Circulating Current Suppression in Multiparalleled Three-Phase Inverters," IEEE Transactions on Industrial Electronics, vol. 64, no. 1, pp. 838-847, Jan. 2017.
[29] Z. Liu, J. Liu, X. Hou, Q. Dou, D. Xue, and T. Liu, "Output Impedance Modeling and Stability Prediction of Three-Phase Paralleled Inverters With Master–Slave Sharing Scheme Based on Terminal Characteristics of Individual Inverters," IEEE Transactions on Power Electronics, vol. 31, no. 7, pp. 5306-5320, Jul. 2016.
[30] Y. Qi, Y. Tang, K. R. R. Potti, and K. Rajashekara, "Robust Power Sharing Control for Parallel Three-phase Inverters Against Voltage Measurement Errors," IEEE Transactions on Power Electronics, vol. 35, no. 12, pp. 13590-13601, Dec. 2020.
[31] E. Lenz, D. J. Pagano, A. Ruseler, and M. L. Heldwein, "Two-Parameter Stability Analysis of Resistive Droop Control Applied to Parallel-Connected Voltage-Source Inverters," IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 8, no. 4, pp. 3318-3332, Dec. 2020.
[32] J. A. P. Lopes, C. L. Moreira and A. G. Madureira, "Defining control strategies for MicroGrids islanded operation," IEEE Transactions on Power Systems, vol. 21, no. 2, pp. 916-924, May 2006.
[33] S. Sen and V. Kumar, "Decentralized Output-Feedback-Based Robust LQR V-f Controller for PV-Battery Microgrid Including Generation Uncertainties," IEEE Systems Journal, vol. 14, no. 3, pp. 4418-4429, Sep. 2020.
[34] J. M. Guerrero, L. G. de Vicuna, J. Matas, M. Castilla, and J. Miret, "A wireless controller to enhance dynamic performance of parallel inverters in distributed generation systems," IEEE Transactions on Power Electronics, vol. 19, no. 5, pp. 1205-1213, Sep. 2004.
[35] Y. Han, H. Li, P. Shen, E. A. A. Coelho, and J. M. Guerrero, "Review of Active and Reactive Power Sharing Strategies in Hierarchical Controlled Microgrids," IEEE Transactions on Power Electronics, vol. 32, no. 3, pp. 2427-2451, Mar. 2017.
[36] S. Anand, B. G. Fernandes and J. Guerrero, "Distributed Control to Ensure Proportional Load Sharing and Improve Voltage Regulation in Low-Voltage DC Microgrids," IEEE Transactions on Power Electronics, vol. 28, no. 4, pp. 1900-1913, Apr. 2013.
[37] X. Lu, J. M. Guerrero, K. Sun, J. C. Vasquez, R. Teodorescu, and L. Huang, "Hierarchical Control of Parallel AC-DC Converter Interfaces for Hybrid Microgrids," IEEE Transactions on Smart Grid, vol. 5, no. 2, pp. 683-692, Mar. 2014.
[38] I. Chung, W. Liu, D. A. Cartes, E. G. Collins, and S. Moon, "Control Methods of Inverter-Interfaced Distributed Generators in a Microgrid System," IEEE Transactions on Industry Applications, vol. 46, no. 3, pp. 1078-1088, May-Jun. 2010.
[39] C. Wang, Y. Li, K. Peng, B. Hong, Z. Wu, and C. Sun, "Coordinated Optimal Design of Inverter Controllers in a Micro-Grid with Multiple Distributed Generation Units," IEEE Transactions on Power Systems, vol. 28, no. 3, pp. 2679-2687, Aug. 2013.
[40] S. Adhikari and F. Li, "Coordinated V-f and P-Q Control of Solar Photovoltaic Generators With MPPT and Battery Storage in Microgrids," IEEE Transactions on Smart Grid, vol. 5, no. 3, pp. 1270-1281, May 2014.
[41] X. Tang, X. Hu, N. Li, W. Deng, and G. Zhang, "A Novel Frequency and Voltage Control Method for Islanded Microgrid Based on Multienergy Storages," IEEE Transactions on Smart Grid, vol. 7, no. 1, pp. 410-419, Jan. 2016.
[42] Y.-Y. Tzou, "DSP-based fully digital control of a PWM DC-AC converter for AC voltage regulation," Proceedings of PESC '95 - Power Electronics Specialist Conference, pp. 138-144 vol.1, 1995.
[43] X. Wang, P. C. Loh and F. Blaabjerg, "Stability Analysis and Controller Synthesis for Single-Loop Voltage-Controlled VSIs," IEEE Transactions on Power Electronics, vol. 32, no. 9, pp. 7394-7404, Sep. 2017.
[44] Y. Guan, Y. Wang, Y. Xie, Y. Liang, A. Lin, and X. Wang, "The Dual-Current Control Strategy of Grid-Connected Inverter with LCL Filter," IEEE Transactions on Power Electronics, vol. 34, no. 6, pp. 5940-5952, Jun. 2019.
[45] O. Kukrer, S. Bayhan and H. Komurcugil, "Model-Based Current Control Strategy with Virtual Time Constant for Improved Dynamic Response of Three-Phase Grid-Connected VSI," IEEE Transactions on Industrial Electronics, vol. 66, no. 6, pp. 4156-4165.
[46] P. C. Loh and D. G. Holmes, "Analysis of multiloop control strategies for LC/CL/LCL-filtered voltage-source and current-source inverters," IEEE Transactions on Industry Applications, vol. 41, no. 2, pp. 644-654, Mar.-Apr. 2005.
[47] Z. Xin, X. Wang, P. C. Loh, and F. Blaabjerg, "Grid-Current-Feedback Control for LCL-Filtered Grid Converters with Enhanced Stability," IEEE Transactions on Power Electronics, vol. 32, no. 4, pp. 3216-3228, Apr. 2017.
[48] J. Rodriguez et al., "Predictive Current Control of a Voltage Source Inverter," IEEE Transactions on Industrial Electronics, vol. 54, no. 1, pp. 495-503, Feb. 2007.
[49] S. Buso, T. Caldognetto and D. I. Brandao, "Dead-Beat Current Controller for Voltage-Source Converters with Improved Large-Signal Response," IEEE Transactions on Industry Applications, vol. 52, no. 2, pp. 1588-1596, Mar.-Apr. 2016.
[50] T.-F. Wu, L.-C. Lin, N. Yao, Y.-K. Chen, and Y.-C. Chang, "Extended Application of D-Σ Digital Control to a Single-Phase Bidirectional Inverter with an LCL Filter," IEEE Transactions on Power Electronics, vol. 30, no. 7, pp. 3903-3911, Jul. 2015.
[51] P. Mattavelli, "Synchronous-frame harmonic control for high-performance AC power supplies," IEEE Transactions on Industry Applications, vol. 37, no. 3, pp. 864-872, May-Jun. 2001.
[52] S. Yang, Q. Lei, F. Z. Peng, and Z. Qian, "A Robust Control Scheme for Grid-Connected Voltage-Source Inverters," IEEE Transactions on Industrial Electronics, vol. 58, no. 1, pp. 202-212, Jan. 2011.
[53] Q. Zhong and T. Hornik, "Cascaded Current–Voltage Control to Improve the Power Quality for a Grid-Connected Inverter with a Local Load," IEEE Transactions on Industrial Electronics, vol. 60, no. 4, pp. 1344-1355, Apr. 2013.
[54] Y.-Y. Tzou and S.-Y. Lin, "Fuzzy-tuning current-vector control of a three-phase PWM inverter for high-performance AC drives," IEEE Transactions on Industrial Electronics, vol. 45, no. 5, pp. 782-791, Oct. 1998.
[55] H. Komurcugil, S. Bayhan and H. Abu-Rub, "Variable- and Fixed-Switching-Frequency-Based HCC Methods for Grid-Connected VSI with Active Damping and Zero Steady-State Error," IEEE Transactions on Industrial Electronics, vol. 64, no. 9, pp. 7009-7018, Sep. 2017.
[56] R. Giri, V. Choudhary, R. Ayyanar, and N. Mohan, "Common-duty-ratio control of input-series connected modular DC-DC converters with active input voltage and load-current sharing," IEEE Transactions on Industry Applications, vol. 42, no. 4, pp. 1101-1111, Jul.-Aug. 2006.
[57] J. Shi, J. Luo and X. He, "Common-Duty-Ratio Control of Input-Series Output-Parallel Connected Phase-shift Full-Bridge DC–DC Converter Modules," IEEE Transactions on Power Electronics, vol. 26, no. 11, pp. 3318-3329, Nov. 2011.
[58] D. Sha, Z. Guo and X. Liao, "Control Strategy for Input-Parallel–Output-Parallel Connected High-Frequency Isolated Inverter Modules," IEEE Transactions on Power Electronics, vol. 26, no. 8, pp. 2237-2248, Aug. 2011.
[59] J. M. Guerrero, L. Hang and J. Uceda, "Control of Distributed Uninterruptible Power Supply Systems," IEEE Transactions on Industrial Electronics, vol. 55, no. 8, pp. 2845-2859, Aug. 2008.
[60] Z. Xueguang, Z. Wenjie, C. Jiaming, and X. Dianguo, "Deadbeat Control Strategy of Circulating Currents in Parallel Connection System of Three-Phase PWM Converter," IEEE Transactions on Energy Conversion, vol. 29, no. 2, pp. 406-417, Jun. 2014.
[61] X. Xing, Z. Zhang, C. Zhang, J. He, and A. Chen, "Space Vector Modulation for Circulating Current Suppression Using Deadbeat Control Strategy in Parallel Three-Level Neutral-Clamped Inverters," IEEE Transactions on Industrial Electronics, vol. 64, no. 2, pp. 977-987, Feb. 2017.
[62] A. M. Roslan, K. H. Ahmed, S. J. Finney, and B. W. Williams, "Improved Instantaneous Average Current-Sharing Control Scheme for Parallel-Connected Inverter Considering Line Impedance Impact in Microgrid Networks," IEEE Transactions on Power Electronics, vol. 26, no. 3, pp. 702-716, Mar. 2011.
[63] Y. Zhang, M. Yu, F. Liu, and Y. Kang, "Instantaneous Current-Sharing Control Strategy for Parallel Operation of UPS Modules Using Virtual Impedance," IEEE Transactions on Power Electronics, vol. 28, no. 1, pp. 432-440, Jan. 2013.
[64] S. Tolani and P. Sensarma, "An Instantaneous Average Current Sharing Scheme for Parallel UPS Modules," IEEE Transactions on Industrial Electronics, vol. 64, no. 12, pp. 9210-9220, Dec. 2017.
[65] S. K. Mazumder, M. Tahir and K. Acharya, "Master–Slave Current-Sharing Control of a Parallel DC–DC Converter System Over an RF Communication Interface," IEEE Transactions on Industrial Electronics, vol. 55, no. 1, pp. 59-66, Jan. 2008.
[66] M. Borrega, L. Marroyo, R. González, J. Balda, and J. L. Agorreta, "Modeling and Control of a Master–Slave PV Inverter with N-Paralleled Inverters and Three-Phase Three-Limb Inductors," IEEE Transactions on Power Electronics, vol. 28, no. 6, pp. 2842-2855, Jun. 2013.
[67] T.-F. Wu, Y.-K. Chen and Y.-H. Huang, "3C strategy for inverters in parallel operation achieving an equal current distribution," IEEE Transactions on Industrial Electronics, vol. 47, no. 2, pp. 273-281, Apr. 2000.
[68] X. Yu, A. M. Khambadkone, H. Wang, and S. T. S. Terence, "Control of Parallel-Connected Power Converters for Low-Voltage Microgrid—Part I: A Hybrid Control Architecture," IEEE Transactions on Power Electronics, vol. 25, no. 12, pp. 2962-2970, Dec. 2010.
[69] J. He, Y. W. Li and F. Blaabjerg, "An Enhanced Islanding Microgrid Reactive Power, Imbalance Power, and Harmonic Power Sharing Scheme," IEEE Transactions on Power Electronics, vol. 30, no. 6, pp. 3389-3401, Jun. 2015.
[70] L. Shu, W. Chen and X. Jiang, "Decentralized Control for Fully Modular Input-Series Output-Parallel (ISOP) Inverter System Based on the Active Power Inverse-Droop Method," IEEE Transactions on Power Electronics, vol. 33, no. 9, pp. 7521-7530, Sep. 2018.
[71] J. Sun, “Impedance-based stability criterion for grid-connected inverters,” IEEE Transactions on Power Electronics, vol. 26, no. 11, pp. 3075–3078, Nov. 2011.
[72] A. Reznik, M. G. Simões, A. Al-Durra, and S. M. Muyeen, "LCL Filter Design and Performance Analysis for Grid-Interconnected Systems," IEEE Transactions on Industry Applications, vol. 50, no. 2, pp. 1225-1232, Mar.-Apr. 2014.
[73] Chang Sung Corporation, “Soft Magnetic Powder Cores Ver.02,” e-catalog, Sept. 2018.
[74] K. Venkatachalam, C. R. Sullivan, T. Abdallah, and H. Tacca, "Accurate prediction of ferrite core loss with nonsinusoidal waveforms using only Steinmetz parameters," 2002 IEEE Workshop on Computers in Power Electronics, pp. 36-41, 2002.
[75] Infineon, “62mm C-series module with fast trench/fieldstop IGBT4 and Emitter Controlled diode,” FF450R12KT4 datasheet, Nov. 2008 [revision 2.3].
[76] Infineon, “PrimePACK™2 module with Trench / Fieldstop IGBT4 and Emitter Controlled diode,” FF900R12IE4VP datasheet, Aug. 2016 [revision V3.0].
[77] ROHM, “SiC Power Module,” BSM400D12P2G003 datasheet, Feb. 2018 [Rev.001].
[78] Infineon, “PrimePACK™2 module with Trench / Fieldstop IGBT4 and Emitter Controlled 4 diode and NTC,” FF600R12IP4 datasheet, Nov. 2013 [revision 2.4].
[79] Infineon, “Easy DUAL module with CoolSiC™ Trench MOSFET and PressFIT / NTC,” FF6MR12W2M1_B11 datasheet, May. 2019 [revision V2.1].
[80] H. Hu, Z. He, X. Li, K. Wang, and S. Gao, "Power-Quality Impact Assessment for High-Speed Railway Associated with High-Speed Trains Using Train Timetable—Part I: Methodology and Modeling," IEEE Transactions on Power Delivery, vol. 31, no. 2, pp. 693-703, Apr. 2016.
[81] H. Sung, N. Jung, and S. Huang et al. Application of Social Spider Algorithm to Optimize Train Energy. J. Electr. Eng. Technol. 14, pp. 519–526, 2019.
[82] C.-T. Pan and Y.-H. Liao, "Modeling and Control of Circulating Currents for Parallel Three-Phase Boost Rectifiers with Different Load Sharing," IEEE Transactions on Industrial Electronics, vol. 55, no. 7, pp. 2776-2785, Jul. 2008.
[83] "IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems," IEEE Std 519-2014 (Revision of IEEE Std 519-1992), vol., no., pp.1-29, 11 Jun. 2014.
[84] IEC 62040-3, “Uninterruptible power systems (UPS) – Part 3: Method of specifying the performance and test requirements. International Electrotechnical Commission,” Geneva, Switzerland, 2011.