本論文提出一種耦合型穩定度分析方法，分析三相四線式與三相三線式系統之三相電流追蹤能力及系統之穩定度。此外，比較耦合型與電路等效單相之解耦合穩定度分析，個別應用在三相四線式及三相三線式轉換器之間差異，並考慮濾波器電感值隨電流大小的變化，搭配解耦合數位控制與濾波器設計，實現三相高功率併網型轉換器。本論文透過平均共模電壓觀念，設計電流控制演算法，並藉由時域及頻域推導出轉換器輸入對輸出之轉移函數，用於分析系統穩定度與設計濾波器，最後實測驗證轉換器功能。
在穩定度分析比較方面，本論文各別推導出三相四線式LC與三相三線式LCL轉換器之輸入對輸出轉移函數，從相對簡易的三相四線式轉換器至複雜的三相三線式轉換器，比較耦合型與解耦合型轉移函數間之差異和考慮電感值衰減的影響。同時為了驗證轉移函數的正確性，本研究將三相系統建模於MATLAB中，並以MATLAB/Simscape模型結果為基準，比較模型結果與推導結果的一致性。此外，基於濾波器諧振頻帶穩定性，本論文提出三相三線式LCL轉換器濾波器設計，考慮電感值不同的衰減量與濾波器總體積大小，並且透過供應商提供的鐵芯參數，設計出濾波器各元件值並篩選出符合使用者所需規格限制下的鐵芯元件。
在系統功能驗證方面，受限於環境容量，本研究建造二部DC 760V/ac 380V/350 kVA的三相四線式LC轉換器，透過實際二部循環功率測試以驗證市電併網與直流鏈電壓穩壓功能。此外，亦建造一部DC 760V/ac 380V/33 kVA的三相三線式LCL轉換器並實際測試市電併網與直流鏈電壓穩壓功能，最後實現多部轉換器並聯並測試。同時，本研究建立MATLAB/Simulink模擬模型，比對在相同規格下的三相四線式與三相三線式轉換器實測驗證結果與模擬結果，驗證Simulink模型與實測結果的一致性。
透過模擬與實測結果，本論文驗證三相耦合型穩定度分析，具有更高的精確性並更符合電路實際運作等優點，此外，配合濾波器設計與解耦合數位控制可減少濾波器體積並使輸出電流符合IEEE Std 519-2014 和IEEE Std 1547之電流注入電網諧波規範。
本論文的原創性貢獻簡述如下：
本論文所提出的三相三線式轉換器耦合型穩定度分析，相較於傳統解耦合型穩定度分析，與MATLAB/Simscape模型結果一致。
耦合型穩定度分析將電感值衰減量和市電電網強度納入變化因素，分析當電感值隨電流大小變化時之影響與系統的穩定性。
三相三線式轉換器LCL濾波器設計方法配合耦合型穩定度分析，將供應商提供的鐵芯參數納入考量並計算鐵芯體積，設計出符合使用者所需之濾波器元件參數值。
以「直接數位控制」的三相轉換器電流控制演算法，配合耦合型穩定度分析，確保實測有低輸出電流總諧波失真率且穩定操作，滿足IEEE Std 519-2014 和IEEE Std 1547的諧波規範。
藉由提高開關切換頻率，以降低濾波器體積且提升系統動態響應，在系統穩定運行下，實測多部並聯以提高整體系統額定功率。

This dissertation proposes a coupled stability analysis to analyze the three-phase current tracking capability and the system stability of the three-phase four-wire (3Ф4W) and three-phase three-wire (3Ф3W) systems. In addition, it compares the difference between the coupled and equivalent-circuit decoupled stability analyses for 3Ф4W and 3Ф3W converters. Moreover, it considers filter inductance variations simultaneously to verify a three-phase grid-connected converter with decoupled digital control (DDC) and filter design. The current control algorithm based on the concept of the average common-mode voltage (ACMV), system parameters, and the input-to-output transfer functions of the converters are derived and analyzed with time-domain and frequency-domain models.
For the stability analyses, the transfer functions of the 3Ф4W LC and 3Ф3W LCL converters are derived. The differences between the coupled and decoupled transfer functions with wide filter inductance variation and distorted grid voltages are compared and discussed from a relatively simple 3Ф4W converter to a complex 3Ф3W converter. In order to verify the correctness of the transfer functions, the three-phase system is modeled in MATLAB, and the results of the MATLAB/Simscape model with the linear analysis tool are used as a benchmark to compare the consistency of the model with the derived results. Besides, based on the stability of the resonant frequency band, the filter design of a 3Ф3W converter by considering inductance variations and the total volume of the filter is proposed. Moreover, the filter and core-element parameters are designed and filtered to meet the user requirements.
To verify and develop the system transfer functions, two DC 760V/ac 380V/350 kVA 3Ф4W LC converters were built to confirm the grid connection and DC-bus voltage regulation with the circulating power test (CPT) set-up due to the limited environmental capacity. In addition, a 3Ф3W LCL converter with DC 760V/ac 380V/33 kVA was built and tested for the grid-connected functions; moreover, multiple converters in parallel were constructed and tested. In this dissertation, a MATLAB Simulink simulation model was built and analyzed to compare the simulated and experimental results of the 3Ф4W and 3Ф3W converters with the exact specifications.
Finally, based on simulated and experimental results, the three-phase coupled stability analyses are verified and analyzed to be more accurate and consistent with actual circuit operation. Besides, the filter design and DDC can reduce the filter volume and make the output current total harmonic distortions (THDs) comply with the IEEE-519-2014 and IEEE-1547 harmonic standards.
The original contributions of this dissertation are briefly presented as follows:
Compared with the traditional decoupled stability analyses, the proposed coupled stability analyses of the 3Ф3W LCL converters are consistent with the results of MATLAB/Simscape model.
The proposed coupled stability analyses incorporate the wide inductance variation and analyze the effect of the system stability. Besides, depending on the different grid conditions, the accuracy of the proposed coupled stability analyses is improved compared to the decoupled stability analyses.
The filter design of 3Ф3W converter with coupled stability analyses takes the core parameters provided by the manufacturer into consideration. It calculates the core volume to design the filter parameters that meet user needs.
The derived simple three-phase converter current control algorithms with coupled stability analyses can ensure low THDs of output current and compliance with the IEEE-519-2014 and IEEE-1547 harmonic standards.
By increasing the switching frequency, the filter volume can be reduced, and the system dynamic response can be improved. Simulated and experimental results of two filter parameters are verified and compared. In addition, the overall system power rating is increased by multiple converters in parallel under stable operation.

中文摘要-------------------------------------------------------------i
ABSTRACT-----------------------------------------------------------iii
ACKNOWLEDGEMENTS----------------------------------------------------vi
TABLE OF CONTENTS-------------------------------------------------viii
LIST OF FIGURES-----------------------------------------------------xi
LIST OF TABLES-----------------------------------------------------xix
LIST OF ABBREVIATIONS----------------------------------------------xxi
CHAPTER 1 INTRODUCTION-----------------------------------------------1
1.1 Background and Motivation----------------------------------------1
1.2 Review of Previous Work------------------------------------------3
1.2.1 Control Approach-----------------------------------------------3
1.2.2 Filter Design--------------------------------------------------5
1.2.3 Stability Analysis of the System-------------------------------8
1.3 Dissertation Outline---------------------------------------------9
CHAPTER 2 CONTROL ALGORITHMS FOR THE 3Ф4W LC AND 3Ф3W LCL CONVERTERS----------------------------------------------------------------------12
2.1 Control for the 3Ф4W LC Converter-------------------------------12
2.1.1 Structure for the 3Ф4W LC Converter with CPT------------------13
2.1.2 Derivation of Control Laws for the 3Ф4W LC Converter----------14
2.1.3 Communication, Start-up, and Test Process---------------------17
2.2 Control for the 3Ф3W LCL Converter------------------------------19
2.2.1 Derivation of Current Control for the 3Ф3W LCL Converter------19
2.2.2 Communication, Test, and Start-up Process for Single and Multiple Converters-------------------------------------------------27
2.2.3 Derivation of Voltage Control for the 3Ф3W LCL Converter------27
2.2.4 Test and Start-up Process for the DC-bus Voltage Regulation---30
2.3 Discussion------------------------------------------------------31
CHAPTER 3 FILTER DESIGN---------------------------------------------33
3.1 LC Filter Design for the 3Ф4W Converter-------------------------33
3.1.1 Design Example with a 350 kVA 3Ф4W LC Converter---------------34
3.2 LCL Filter Design for the 3Ф3W Converter------------------------35
3.2.1 Converter-side Inductor Design--------------------------------36
3.2.2 Grid-side Inductor Design-------------------------------------41
3.2.3 Filter Capacitor Design---------------------------------------42
3.2.4 Limitations of the Designed Filter Parameters-----------------43
3.2.5 Filter Design Procedure---------------------------------------49
3.2.6 Design Example with a 33 kVA 3Ф3W LCL Converter---------------55
3.3 Discussion------------------------------------------------------58
CHAPTER 4 CURRENT TRACKING CAPABILITY AND STABILITY ANALYSES OF 3Ф4W LC AND 3Ф3W LCL CONVERTERS------------------------------------------59
4.1 Analyses of the 3Ф4W LC Converter-------------------------------60
4.1.1 Current Tracking Capability-----------------------------------61
4.1.2 System Stability----------------------------------------------65
4.1.3 Comparison of the Stability for Inductance Variation----------68
4.2 Analyses of the 3Ф3W LCL Converter------------------------------70
4.2.1 Derivation of Input-to-output Current Transfer Function-------71
4.2.2 Performance Comparison Between Two Types of Control Laws------78
4.2.3 Stability Comparison Between Coupled and Decoupled Analytical Approaches----------------------------------------------------------84
4.3 Discussion------------------------------------------------------95
CHAPTER 5 SIMULATIONS AND EXPERIMENTAL VALIDATIONS OF THE 3Ф4W LC AND 3Ф3W LCL CONVERTERS-------------------------------------------------96
5.1 Validation of the 3Φ4W LC Converter-----------------------------96
5.1.1 Practical Considerations and Solutions------------------------97
5.1.2 Power Injection and Current Tracking--------------------------99
5.1.3 DC-link Voltage Regulation-----------------------------------104
5.2 Validation of the 3Φ3W LCL Converter---------------------------107
5.2.1 Practical Considerations and Solutions-----------------------109
5.2.2 Power Injection with Two Scenarios---------------------------111
5.2.3 DC-link Voltage Regulation-----------------------------------117
5.2.4 Three Converters in Parallel---------------------------------121
5.3 Discussion-----------------------------------------------------126
CHAPTER 6 CONCLUSIONS AND FUTURE RESEARCHES------------------------128
6.1 Conclusions----------------------------------------------------128
6.2 Future Researches----------------------------------------------130
References---------------------------------------------------------132
VITA---------------------------------------------------------------143
PUBLICATIONS-------------------------------------------------------143

[1] J. Wang, K. Sun, H. Wu, J. Zhu, Y. Xing, and Y. Li, "Hybrid Connected Unified Power Quality Conditioner Integrating Distributed Generation with Reduced Power Capacity and Enhanced Conversion Efficiency," in IEEE Transactions on Industrial Electronics, vol. 68, no. 12, pp. 12340-12352, Dec. 2021.
[2] F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus, "Overview of Control and Grid Synchronization for Distributed Power Generation Systems," in IEEE Transactions on Industrial Electronics, vol. 53, no. 5, pp. 1398-1409, Oct. 2006.
[3] T. Zhou and B. Francois, "Energy Management and Power Control of a Hybrid Active Wind Generator for Distributed Power Generation and Grid Integration," in IEEE Transactions on Industrial Electronics, vol. 58, no. 1, pp. 95-104, Jan. 2011.
[4] R. N. Beres, X. Wang, M. Liserre, F. Blaabjerg, and C. L. Bak, "A Review of Passive Power Filters for Three-Phase Grid-Connected Voltage-Source Converters," in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 4, no. 1, pp. 54-69, March 2016.
[5] A. B. Nassif, W. Xu, and W. Freitas, "An Investigation on the Selection of Filter Topologies for Passive Filter Applications," in IEEE Transactions on Power Delivery, vol. 24, no. 3, pp. 1710-1718, July 2009.
[6] U. P. Yagnik and M. D. Solanki, "Comparison of L, LC & LCL Filter for Grid Connected Converter," 2017 International Conference on Trends in Electronics and Informatics (ICEI), Tirunelveli, India, 2017, pp. 455-458.
[7] W. Choi, C. Lam, M. Wong, and Y. Han, "Analysis of DC-Link Voltage Controls in Three-Phase Four-Wire Hybrid Active Power Filters," in IEEE Transactions on Power Electronics, vol. 28, no. 5, pp. 2180-2191, May 2013.
[8] Y. Zhang, X. Zhou, Y. Chen, and S. Lu, "Three-Phase Four-Wire LCL Filter Active Damping Control Based on Common Mode Capacitor Current Feedback," 2021 6th International Conference on Power and Renewable Energy (ICPRE), Shanghai, China, 2021, pp. 328-332.
[9] S. Bosch, J. Staiger, and H. Steinhart, "Predictive Current Control for an Active Power Filter with LCL-Filter," in IEEE Transactions on Industrial Electronics, vol. 65, no. 6, pp. 4943-4952, June 2018.
[10] M. Nauman and A. Hasan, "Efficient Implicit Model-Predictive Control of a Three-Phase Inverter with an Output LC Filter," in IEEE Transactions on Power Electronics, vol. 31, no. 9, pp. 6075-6078, Sept. 2016.
[11] J. Dannehl, M. Liserre, and F. W. Fuchs, "Filter-Based Active Damping of Voltage Source Converters with LCL Filter," in IEEE Transactions on Industrial Electronics, vol. 58, no. 8, pp. 3623-3633, Aug. 2011.
[12] G. Shen, X. Zhu, J. Zhang, and D. Xu, "A New Feedback Method for PR Current Control of LCL-Filter-Based Grid-Connected Inverter," in IEEE Transactions on Industrial Electronics, vol. 57, no. 6, pp. 2033-2041, June 2010.
[13] H. Nian, Y. Liao, M. Li, D. Sun, Y. Xu, and B. Hu, "Impedance Modeling and Stability Analysis of Three-Phase Four-Leg Grid-Connected Inverter Considering Zero-Sequence," in IEEE Access, vol. 9, pp. 83676-83687, 2021.
[14] J. Zhao, M. Huang, H. Yan, C. K. Tse, and X. Zha, "Nonlinear and Transient Stability Analysis of Phase-Locked Loops in Grid-Connected Converters," in IEEE Transactions on Power Electronics, vol. 36, no. 1, pp. 1018-1029, Jan. 2021.
[15] J. Sun, "Impedance-Based Stability Criterion for Grid-Connected Inverters," in IEEE Transactions on Power Electronics, vol. 26, no. 11, pp. 3075-3078, Nov. 2011.
[16] Y. Wang, X. Wang, Z. Chen, and F. Blaabjerg, "Small-Signal Stability Analysis of Inverter-Fed Power Systems Using Component Connection Method," in IEEE Transactions on Smart Grid, vol. 9, no. 5, pp. 5301-5310, Sept. 2018.
[17] B. Zhang, X. Du, J. Zhao, J. Zhou, and X. Zou, "Impedance Modeling and Stability Analysis of a Three-phase Three-level NPC Inverter Connected to the Grid," in CSEE Journal of Power and Energy Systems, vol. 6, no. 2, pp. 270-278, June 2020.
[18] B. Wen, D. Dong, D. Boroyevich, R. Burgos, P. Mattavelli, and Z. Shen, "Impedance-Based Analysis of Grid-Synchronization Stability for Three-Phase Paralleled Converters," in IEEE Transactions on Power Electronics, vol. 31, no. 1, pp. 26-38, Jan. 2016.
[19] J. He, Y. W. Li, D. Xu, X. Liang, B. Liang, and C. Wang, "Deadbeat Weighted Average Current Control with Corrective Feed-Forward Compensation for Microgrid Converters with Nonstandard LCL Filter," in IEEE Transactions on Power Electronics, vol. 32, no. 4, pp. 2661-2674, April 2017.
[20] D. N. Zmood and D. G. Holmes, "Stationary Frame Current Regulation of PWM Inverters with Zero Steady-state Error," in IEEE Transactions on Power Electronics, vol. 18, no. 3, pp. 814-822, May 2003.
[21] M. S. Zaky and M. K. Metwaly, "A Performance Investigation of a Four-Switch Three-Phase Inverter-Fed IM Drives at Low Speeds Using Fuzzy Logic and PI Controllers," in IEEE Transactions on Power Electronics, vol. 32, no. 5, pp. 3741-3753, May 2017.
[22] E. Tomaszewski and J. Jiangy, "An Anti-Windup Scheme for Proportional Resonant Controllers with Tuneable Phase-shift in Voltage Source Converters," 2016 IEEE Power and Energy Society General Meeting (PESGM), Boston, MA, USA, 2016, pp. 1-5.
[23] N. Panten, N. Hoffmann and F. W. Fuchs, "Finite Control Set Model Predictive Current Control for Grid-Connected Voltage-Source Converters with LCL Filters: A Study Based on Different State Feedbacks," in IEEE Transactions on Power Electronics, vol. 31, no. 7, pp. 5189-5200, July 2016.
[24] O. Vodyakho and C. C. Mi, "Three-Level Inverter-Based Shunt Active Power Filter in Three-Phase Three-Wire and Four-Wire Systems," in IEEE Transactions on Power Electronics, vol. 24, no. 5, pp. 1350-1363, May 2009.
[25] J. Ge, Z. Shuai, H. Zhao, and Z. J. Shen, "Generalized Power and Current Control for Three-Phase Four-Wire Converter under Unbalanced Grid Conditions," IECON 2019 - 45th Annual Conference of the IEEE Industrial Electronics Society, Lisbon, Portugal, 2019, pp. 3900-3905.
[26] R. Teodorescu, M. Liserre, and P. Rodríguez, Grid Converters for Photovoltaic and Wind Power Systems. Chichester, UK: John Wiley & Sons, 2011, p. 169-245.
[27] N. Altin, S. Ozdemir, H. Komurcugil, and I. Sefa, "Sliding-Mode Control in Natural Frame with Reduced Number of Sensors for Three-Phase Grid-Tied LCL-Interfaced Inverters," in IEEE Transactions on Industrial Electronics, vol. 66, no. 4, pp. 2903-2913, April 2019.
[28] S. Mariethoz and M. Morari, "Explicit Model-Predictive Control of a PWM Inverter with an LCL Filter," in IEEE Transactions on Industrial Electronics, vol. 56, no. 2, pp. 389-399, Feb. 2009.
[29] M. G. Judewicz, S. A. González, J. R. Fischer, J. F. Martínez, and D. O. Carrica, "Inverter-Side Current Control of Grid-Connected Voltage Source Inverters with LCL Filter Based on Generalized Predictive Control," in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 6, no. 4, pp. 1732-1743, Dec. 2018.
[30] Y. He, H. S.-H. Chung, C. N.-M. Ho, and W. Wu, "Use of Boundary Control with Second-Order Switching Surface to Reduce the System Order for Deadbeat Controller in Grid-Connected Inverter," in IEEE Transactions on Power Electronics, vol. 31, no. 3, pp. 2638-2653, March 2016.
[31] Y. He, H. S.-h. Chung, C. N.-M. Ho, and W. Wu, "Direct Current Tracking Using Boundary Control with Second-Order Switching Surface for Three-Phase Three-Wire Grid-Connected Inverter," in IEEE Transactions on Power Electronics, vol. 32, no. 7, pp. 5723-5740, July 2017.
[32] C. A. Busada, S. Gomez Jorge, and J. A. Solsona, "Full-State Feedback Equivalent Controller for Active Damping in LCL-Filtered Grid-Connected Inverters Using a Reduced Number of Sensors," in IEEE Transactions on Industrial Electronics, vol. 62, no. 10, pp. 5993-6002, Oct. 2015.
[33] T.-F. Wu, H.-C. Hsieh, C.-H. Chang, L.-C. Lin, and Y.-R. Chang, "Improvement of Control Law Derivation and Region Selection for D-Σ Digital Control," in IEEE Transactions on Industrial Electronics, vol. 62, no. 10, pp. 6042-6050, Oct. 2015.
[34] T.-F. Wu, L.-C. Yu, Y.-H. Huang, Y.-Y. Jhang, and B.-T. Zeng, "SPWM-Based Direct Digital Control with Average-Voltage Model and D–Σ Process for Paralleled 3Ф3W Grid-Connected Converters to Reduce Circulating Currents," in IEEE Transactions on Industrial Electronics, vol. 66, no. 6, pp. 4436-4446, June 2019.
[35] T.-F. Wu, M. Misra, Y.-Y. Jhang, Y.-H. Huang, and L.-C. Lin, "Direct Digital Control of Single-Phase Grid-Connected Inverters with LCL Filter Based on Inductance Estimation Model," in IEEE Transactions on Power Electronics, vol. 34, no. 2, pp. 1851-1862, Feb. 2019.
[36] K. H. Ahmed, S. J. Finney, and B. W. Williams, "Passive Filter Design for Three-Phase Inverter Interfacing in Distributed Generation," 2007 Compatibility in Power Electronics, Gdansk, Poland, 2007, pp. 1-9.
[37] C. Vadstrup, X. Wang, and F. Blaabjerg, "LC Filter Design for Wide Band Gap Device Based Adjustable Speed Drives," 2014 International Power Electronics and Application Conference and Exposition, Shanghai, China, 2014, pp. 1291-1296.
[38] P. A. Dahono, A. Purwadi, and Qamaruzzaman, "An LC Filter Design Method for Single-phase PWM Inverters," Proceedings of 1995 International Conference on Power Electronics and Drive Systems. PEDS 95, Singapore, 1995, pp. 571-576.
[39] Y. Tang, W. Yao, P. C. Loh, and F. Blaabjerg, "Design of LCL Filters with LCL Resonance Frequencies Beyond the Nyquist Frequency for Grid-Connected Converters," in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 4, no. 1, pp. 3-14, March 2016.
[40] R. Peña-Alzola, M. Liserre, F. Blaabjerg, M. Ordonez, and Y. Yang, "LCL-Filter Design for Robust Active Damping in Grid-Connected Converters," in IEEE Transactions on Industrial Informatics, vol. 10, no. 4, pp. 2192-2203, Nov. 2014.
[41] M. Liserre, F. Blaabjerg, and S. Hansen, "Design and Control of an LCL-filter-based Three-phase Active Rectifier," in IEEE Transactions on Industry Applications, vol. 41, no. 5, pp. 1281-1291, Sept.-Oct. 2005.
[42] S. Jayalath and M. Hanif, "An LCL-Filter Design with Optimum Total Inductance and Capacitance," in IEEE Transactions on Power Electronics, vol. 33, no. 8, pp. 6687-6698, Aug. 2018.
[43] T. C. Y. Wang, Zhihong Ye, Gautam Sinha, and Xiaoming Yuan, "Output Filter Design for a Grid-interconnected Three-phase Inverter," IEEE 34th Annual Conference on Power Electronics Specialist, 2003. PESC '03., Acapulco, Mexico, 2003, pp. 779-784.
[44] A. A. Rockhill, M. Liserre, R. Teodorescu, and P. Rodriguez, "Grid-Filter Design for a Multimegawatt Medium-Voltage Voltage-Source Inverter," in IEEE Transactions on Industrial Electronics, vol. 58, no. 4, pp. 1205-1217, April 2011.
[45] P. Channegowda and V. John, "Filter Optimization for Grid Interactive Voltage Source Inverters," in IEEE Transactions on Industrial Electronics, vol. 57, no. 12, pp. 4106-4114, Dec. 2010.
[46] Y. Tang, P. C. Loh, P. Wang, F. H. Choo, F. Gao, and F. Blaabjerg, "Generalized Design of High Performance Shunt Active Power Filter with Output LCL Filter," in IEEE Transactions on Industrial Electronics, vol. 59, no. 3, pp. 1443-1452, March 2012.
[47] A. Cagnano, E. De Tuglie, M. Liserre, and R. A. Mastromauro, "Online Optimal Reactive Power Control Strategy of PV Inverters," in IEEE Transactions on Industrial Electronics, vol. 58, no. 10, pp. 4549-4558, Oct. 2011.
[48] F. Huerta, D. Pizarro, S. Cobreces, F. J. Rodriguez, C. Giron, and A. Rodriguez, "LQG Servo Controller for the Current Control of LCL Grid-Connected Voltage-Source Converters," in IEEE Transactions on Industrial Electronics, vol. 59, no. 11, pp. 4272-4284, Nov. 2012.
[49] Y. Tang, P. C. Loh, P. Wang, F. H. Choo, and F. Gao, "Exploring Inherent Damping Characteristic of LCL-Filters for Three-Phase Grid-Connected Voltage Source Inverters," in IEEE Transactions on Power Electronics, vol. 27, no. 3, pp. 1433-1443, March 2012.
[50] Y. Chen and F. Liu, "Design and Control for Three-Phase Grid-Connected Photovoltaic Inverter with LCL Filter," 2009 IEEE Circuits and Systems International Conference on Testing and Diagnosis, Chengdu, China, 2009, pp. 1-4.
[51] F. Liu, Y. Zhou, S. Duan, J. Yin, B. Liu, and F. Liu, "Parameter Design of a Two-Current-Loop Controller Used in a Grid-Connected Inverter System with LCL Filter," in IEEE Transactions on Industrial Electronics, vol. 56, no. 11, pp. 4483-4491, Nov. 2009.
[52] I. J. Gabe, V. F. Montagner, and H. Pinheiro, "Design and Implementation of a Robust Current Controller for VSI Connected to the Grid Through an LCL Filter," in IEEE Transactions on Power Electronics, vol. 24, no. 6, pp. 1444-1452, June 2009.
[53] M.-Y. Park, M.-H. Chi, J.-H. Park, H.-G. Kim, T.-W. Chun, and E.-C. Nho, "LCL-filter Design for Grid-connected PCS Using Total Harmonic Distortion and Ripple Attenuation Factor," The 2010 International Power Electronics Conference - ECCE ASIA -, Sapporo, Japan, 2010, pp. 1688-1694.
[54] "IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems," in IEEE Std 519-2014 (Revision of IEEE Std 519-1992), vol., no., pp.1-29, 11 June 2014.
[55] "IEEE Standard Conformance Test Procedures for Equipment Interconnecting Distributed Resources with Electric Power Systems," in IEEE Std 1547.1-2005, vol., no., pp.1-62, 1 July 2005.
[56] S. Sen, K. Yenduri, and P. Sensarma, "Step-by-step Design and Control of LCL Filter Based Three Phase Grid-connected Inverter," 2014 IEEE International Conference on Industrial Technology (ICIT), Busan, Korea (South), 2014, pp. 503-508.
[57] T.-F. Wu, M. Misra, L.-C. Lin, and C.-W. Hsu, "An Improved Resonant Frequency Based Systematic LCL Filter Design Method for Grid-Connected Inverter," in IEEE Transactions on Industrial Electronics, vol. 64, no. 8, pp. 6412-6421, Aug. 2017.
[58] A. Reznik, M. G. Simões, A. Al-Durra, and S. M. Muyeen, " LCL Filter Design and Performance Analysis for Grid-Interconnected Systems," in IEEE Transactions on Industry Applications, vol. 50, no. 2, pp. 1225-1232, March-April 2014.
[59] SeungGyu Seo, Yongsoo Cho, and K.-B. Lee, "LCL-filter Design for Grid-connected Three-phase Inverter Using Space Vector PWM," 2016 IEEE 8th International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia), Hefei, China, 2016, pp. 389-394.
[60] Wei Sun, Zhe Chen, and Xiaojie Wu, "Intelligent Optimize Design of LCL Filter for Three-phase Voltage-source PWM Rectifier," 2009 IEEE 6th International Power Electronics and Motion Control Conference, Wuhan, 2009, pp. 970-974.
[61] Y. Ren et al., "A Strictly Sufficient Stability Criterion for Grid-Connected Converters Based on Impedance Models and Gershgorin's Theorem," in IEEE Transactions on Power Delivery, vol. 35, no. 3, pp. 1606-1609, June 2020.
[62] Y. Wang, X. Wang, F. Blaabjerg, and Z. Chen, "Frequency Scanning-based Stability Analysis Method for Grid-connected Inverter System," 2017 IEEE 3rd International Future Energy Electronics Conference and ECCE Asia (IFEEC 2017 - ECCE Asia), Kaohsiung, Taiwan, 2017, pp. 1575-1580.
[63] J. Wang, J. D. Yan, L. Jiang, and J. Zou, "Delay-Dependent Stability of Single-Loop Controlled Grid-Connected Inverters with LCL Filters," in IEEE Transactions on Power Electronics, vol. 31, no. 1, pp. 743-757, Jan. 2016.
[64] J. He and Y. W. Li, "Generalized Closed-Loop Control Schemes with Embedded Virtual Impedances for Voltage Source Converters with LC or LCL Filters," in IEEE Transactions on Power Electronics, vol. 27, no. 4, pp. 1850-1861, April 2012.
[65] D. Pan, X. Ruan, C. Bao, W. Li, and X. Wang, "Capacitor-Current-Feedback Active Damping with Reduced Computation Delay for Improving Robustness of LCL-Type Grid-Connected Inverter," in IEEE Transactions on Power Electronics, vol. 29, no. 7, pp. 3414-3427, July 2014.
[66] J. Wang and J. D. Yan, "Using Virtual Impedance to Analyze the Stability of LCL-filtered Grid-connected Inverters," 2015 IEEE International Conference on Industrial Technology (ICIT), Seville, Spain, 2015, pp. 1220-1225.
[67] W. Jin, Y. Li, G. Sun, X. Chen, and Y. Gao, "Stability Analysis Method for Three-Phase Multi-Functional Grid-Connected Inverters with Unbalanced Local Loads Considering the Active Imbalance Compensation," in IEEE Access, vol. 6, pp. 54865-54875, 2018.
[68] S. Shah and L. Parsa, "Impedance Modeling of Three-Phase Voltage Source Converters in DQ, Sequence, and Phasor Domains," in IEEE Transactions on Energy Conversion, vol. 32, no. 3, pp. 1139-1150, Sept. 2017.
[69] M. Kazem Bakhshizadeh et al., "Couplings in Phase Domain Impedance Modeling of Grid-Connected Converters," in IEEE Transactions on Power Electronics, vol. 31, no. 10, pp. 6792-6796, Oct. 2016.
[70] A. Rygg, M. Molinas, C. Zhang, and X. Cai, "A Modified Sequence-Domain Impedance Definition and Its Equivalence to the dq-Domain Impedance Definition for the Stability Analysis of AC Power Electronic Systems," in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 4, no. 4, pp. 1383-1396, Dec. 2016.
[71] B. Wen, D. Boroyevich, P. Mattavelli, R. Burgos, and Z. Shen, "Modeling the Output Impedance Negative Incremental Resistance Behavior of Grid-tied Inverters," 2014 IEEE Applied Power Electronics Conference and Exposition - APEC 2014, Fort Worth, TX, USA, 2014, pp. 1799-1806.
[72] B. Wen, D. Boroyevich, R. Burgos, P. Mattavelli, and Z. Shen, "Analysis of D-Q Small-Signal Impedance of Grid-Tied Inverters," in IEEE Transactions on Power Electronics, vol. 31, no. 1, pp. 675-687, Jan. 2016.
[73] B. Wen, D. Boroyevich, R. Burgos, P. Mattavelli, and Z. Shen, "Small-Signal Stability Analysis of Three-Phase AC Systems in the Presence of Constant Power Loads Based on Measured d-q Frame Impedances," in IEEE Transactions on Power Electronics, vol. 30, no. 10, pp. 5952-5963, Oct. 2015.
[74] A. Kouchaki, N. F. Javidi, F. Haase, and M. Nymand, "An Analytical Inductor Design Procedure for Three-phase PWM Converters in Power Factor Correction Applications," 2015 IEEE 11th International Conference on Power Electronics and Drive Systems, Sydney, NSW, Australia, 2015, pp. 1013-1018.
[75] M. Liserre, R. Teodorescu, and F. Blaabjerg, "Stability of Photovoltaic and Wind Turbine Grid-connected Inverters for a Large Set of Grid Impedance Values," in IEEE Transactions on Power Electronics, vol. 21, no. 1, pp. 263-272, Jan. 2006.
[76] Chang Sung Corporation, "SOFT MAGNETIC POWDER CORES," ICN, Korea, 2018.
[77] J. J. D’Azzo, C. H. Houpis, and S. N. Sheldon, Linear Control Systems Analysis, and Design with Matlab, 5th ed. New York: Marcel Dekker, 2003.