本論文介紹一系列混合頻率併聯的逆變器系統（HbFPIS）。這種逆變器系統利用基於寬能隙（WBG）材料器件的快速開關能力，以及具高導電性、更成熟、更具成本效益的矽基電晶體元件（如 IGBT）。HbFPIS 是單逆變器系統和相同開關頻率並聯逆變器系統的可行替代方案。可以優化的方面包括開關成本、動態響應和濾波器尺寸。在先前建立的 3P4W HbFPIS 設計技術 [61] 的基礎上，開發並提出了 3P3W HbFPIS 的新技術。
通過詳細的元件設計、開關頻率探討、線上漣波模型和穩定性分析，我們對 HbFPIS 有了更廣闊的認識。本論文詳細介紹載波同步。根據測量波紋和建模波紋之間的比較，提出了載波自動無線同步演算法，從而實現了更加自主的系統。
利用直接數位控制法則和機載漣波模擬，模組可以成功地跟蹤電流指令，為 3P3W 與 3P4W 拓撲提供了用於機載模擬的漣波模型。所提出的系統符合 IEEE-519 標準和漣波衰減函數的動態要求。最後，兩個穩定的三相系統 20 kVA 3P3W 和 30 kVA 3P4W HbFPIS驗證設計過程的完整性。經過證明，HFLPI 能夠自動將其載波與 LFHPI 模組對齊，這表示機載模擬可以多種方式使用，這種能力的主要成果之一是減少模組交互的複雜設計。這可用於自主HFLPI模組，該模組可作為先前非混合逆變器的附加模組運行。
本論文的原創性貢獻包括以下項目：
•  通過成功設計和實現 3P3W HbFPIS，延伸了混合頻率並聯逆變器系統的應用。
•  實現並驗證具有更複雜結構的漣波衰減。
•  提出確保穩定運行、優化漣波衰減和功率調節的設計。
•  介紹基於即時操作紋波模擬和高頻採樣的自動無線載波同步方法，並在模擬和實驗中進行驗證。
•  所提出的控制法、模組之間的互動、濾波器和頻率設計方法，確保輸出總諧波失真率，符合 IEEE-519 標準。

This dissertation presents a family of Hybrid Frequency Parallel Inverter Systems (HbFPIS). Such inverter systems take advantage of the fast switching capability of wide band-gap (WBG) material-based devices and the great conductivity of more mature and more cost-effective silicon-based transistor devices (such as IGBT). HbFPIS is a feasible alternative to single-inverter systems and identical switching frequency parallel inverter systems. The dimensions of possible optimization are switch cost, dynamic response, and filter size. Based on previously established techniques of design of 3P4W HbFPIS [61], new techniques for 3P3W HbFPIS are developed and presented.
With the detailed component design, switching frequencies discussions, online ripple models, and stability analysis, a wider view of HbFPIS is presented. A detailed look at the carrier synchronization is given in this work. With the proposed carrier automatic, the wireless synchronization algorithm based on a comparison between measured ripple and modeled ripple, a more autonomous system is achieved.
Using direct digital control laws together with onboard simulation, the modules can track the current commands successfully. Models of the ripple that are being used for onboard simulation are provided for both 3P3W and 3P4W topologies. Systems resulting from the presented design techniques comply with IEEE-519 standards and with dynamic requirements for ripple attenuation functions. Finally, two examples of stable 20 kVA 3P3W and 30 kVA 3P4W HbFPIS systems have shown the completeness of the design process. The validated capability of HFLPI to autonomously align its carrier with the LFHPI module shows that onboard simulation can be used in multiple ways. One of the main outcomes of such capability is reduced need for complex design of module interaction. This can be used to produce an autonomous HFLPI module that can operate as an add-on module to the previously non-hybrid inverter.
The original contributions of the dissertation include the following items:
 The family of hybrid-frequency parallel inverter systems was expanded with the successful design and implementation of a 3P3W HbFPIS.
 Ripple attenuation with a more complex ripple structure was achieved and verified.
 Design that ensures stable operation, optimized ripple attenuation, and power sharing, is presented.
 The method of automatic and wireless carrier synchronization based on onboard ripple simulation and high-frequency sampling, is presented and verified in simulations and laboratory tests.
 Derived control methods, methods of interaction between modules, filter and frequency design methods ensure the output Total Harmonic Distortion performance complies with IEEE-519 standards.

TABLE OF CONTENTS
中文摘要 i
ABSTRACT iii
ACKNOWLEDGEMENTS v
TABLE OF CONTENTS vi
LIST OF FIGURES ix
LIST OF TABLES xiii
LIST OF ABBREVIATIONS xiv
CHAPTER 1 INTRODUCTION 1
1.1 Background and Motivation 1
1.2 Review of Previous Work 4
1.3 Dissertation Outline 10
CHAPTER 2 CONTROL ALGORITHMS FOR THE 3P4W AND 3P3W HbFPIS 13
2.1 Control Laws for the GC 3P4W and 3P3W HbFPIS 13
2.1.1 Current Controls of 3P4W HbFPIS 15
2.1.2 Current Control of 3P3W HbFPIS 18
2.2 General Inverter Side Inductor Current Ripple Models 21
2.2.1 3P4W Inverter Side Inductor Current Ripple Model 22
2.2.2 3P3W Inverter Side Inductor Current Ripple Model 23
2.2.3 Proposed 3P3W HbFPIS with a Common DC Source Ripple Model 27
2.2.4 Proposed Connection between 3P3W and 3P4W Ripple Models and Concept of Controllability 32
2.3 Automatic Synchronization Based on Ripple Simulation 33
2.3.1 Proposed Time-Domain Cross-Correlation Ripple Matching-Based Synchronization Method 36
2.4 Preprocessing Reference Command 44
2.5 Grid Disturbance Cancellation. 47
2.6 Discussion 48
CHAPTER 3 PARAMETER DESIGN FOR HbFPIS TOPOLOGIES 49
3.1 Design of Switching Frequencies 49
3.2 Filter Parameter Design 53
3.2.1 Inverter-Side Inductance Design for 3P4W HbFPIS 53
3.2.2 Proposed Inverter-Side Inductance Design for 3P3W HbFPIS with Separate DC Sources 55
3.2.3 Proposed Inverter-Side Inductance Design for 3P3W HbFPIS with Common DC Source 56
3.2.4 Permeability Drop Effect 57
3.3 Design of Power-Distribution 58
3.4 Design Examples of 3P3W HbFPIS with Separate DC Sources and 3P4W HbFPIS 60
3.5 Discussion 65
CHAPTER 4 STABILITY ANALYSIS AND CURRENT TRACKING CAPABILITY OF 3P3W AND 3P4W HBFPIS 66
4.1 Proposed Analyses of the 3P3W HbFPIS with Separate DC Sources 66
4.1.1 Current Tracking Capability Analysis 68
4.1.2 Stability Analysis 70
4.2 Analyses of the 3P4W HbFPIS 73
4.2.1 Current Tracking Capability Analysis 74
4.2.2 Stability Analysis 76
4.3 Discussion 78
CHAPTER 5 SIMULATED AND EXPERIMENTAL VERIFICATIONS OF 3P3W AND 3P4W HBFPIS 79
5.1 Practical Considerations 81
5.2 Current Tracking, Ripple Attenuation and Wireless Synchronization Simulations 87
5.3 Grid Connected System Experimental Results 93
5.4 System Stability 96
5.5 Discussion 99
CHAPTER 6 CONCLUSIONS AND FUTURE RESEARCH TOPICS 100
6.1 Conclusions 100
6.2 Future Researches 101
References 103
VITA 113
PUBLICATIONS 113
 
LIST OF FIGURES
Fig. 1.1. The grid-connected (GC) converters in the distributed generation system. 3
Fig. 1.2. Half-bridge hybrid frequency structure. 7
Fig. 1.3. Three-phase three-wire Hybrid-Frequency Parallel-Inverter Systems. 8
Fig. 2.1. System configurations of 3-phase HbFPIS. 15
Fig. 2.2. Equivalent diagram of the 3P4W inverter. 16
Fig. 2.3. Reference values for 3P4W HbFPIS module controllers for full line cycle (A), and quarter cycle(B). 18
Fig. 2.4. Equivalent diagram of the 3P3W inverter. 18
Fig. 2.5. Reference values for 3P3W HbFPIS module controllers for full line cycle (A), and quarter cycle(B). 21
Fig. 2.6. 3P4W inverter side inductor current ripple model. 22
Fig. 2.7. 3P4W inverter side inductor current ripple model. 24
Fig. 2.8. Thévenin equivalent circuits for phase-R for each voltage vector Vi. 26
Fig. 2.9. Circulating current paths. 28
Fig. 2.10. Simplified diagram of circulating current path (A) and equivalent half-bridge connection (B). 29
Fig. 2.11. Simplified diagram of LFHPI current waveform affected by circulation. 29
Fig. 2.12. Synchronization of the carriers of HFLPI and LFHPI. 35
Fig. 2.13. Connection diagram for wired synchronization 36
Fig. 2.14. Connection diagram for wired synchronization 39
Fig. 2.15. Estimated search space for 3P3W ripples at λ=8. 43
Fig. 2.16. Estimated search space for 3P4W ripples at λ=8. 44
Fig. 2.17. From top to bottom: non-inverted control, Feedforward inversion with certain model, Feedforward using inverse and feedback for uncertain model. 45
Fig. 2.18. From top to bottom: full control block diagram, and simplified control block diagram. 46
Fig. 3.1. 3P3W and 3P4W ripples canceled with the same frequency ratio. 50
Fig. 3.2. The average error of reconstruction of ripple signal in 3P3W and 3P4W inverter side inductor. 52
Fig. 3.3. The average error of reconstruction of ripple signal in 3P3W and 3P4W inverter side inductance. 61
Fig. 4.1. System configuration of the Grid-Connected 3Φ3W HbFPIS. 67
Fig. 4.2. Control block diagram of the Grid-Connected 3Φ3W HbFPIS. 68
Fig. 4.3. Bode plots of (4.2) – (4.5) with the parameters as shown in Table 4.1. 70
Fig. 4.4. Small signal equivalent model of grid-connected HbFPIS. 71
Fig. 4.5. Nyquist diagram of open loop representation of grid-connected parallel inverters ηZs. 72
Fig. 4.6. Pole-zero plots of (4.2) – (4.5) transfer functions with the parameters as shown in Table 4.1. 72
Fig. 4.7. System configuration of the Grid-Connected 3Φ3W HbFPIS. 73
Fig. 4.8. Control block diagram of the Grid-Connected 3Φ4W HbFPIS. 74
Fig. 4.9. Bode plots of (4.19) – (4.22) with the parameters as shown in Table 4.1. 75
Fig. 4.10. Nyquist diagram of open loop representation of grid-connected parallel inverters ηZs. 77
Fig. 4.11. Zoomed-on pole-zero plots of (4.19) – (4.22) transfer functions with the parameters as shown in Table 4.2. 78
Fig. 5.1. Laboratory test setup. 79
Fig. 5.2. Experimental setup of GC HbFPIS. 82
Fig. 5.3. FFT of LFHPI inverter side inductor current. 85
Fig. 5.4. LFHPI inverter side current ripples. 86
Fig. 5.5. Superimposed oscilloscope measured ripples (Blue) vs. samples by HFLPI’s controller (Black). 87
Fig. 5.6. Output Voltage and Current (A), LFHPI inverter side current ripples (B) in 3P3W 20 kW GC HbFPIS with separate dc sources. 88
Fig. 5.7. Output Voltage and Current (A), LFHPI inverter side current ripples (B) in 3P4W 30 kW GC HbFPIS. 89
Fig. 5.8. Transient of initial synchronization when local extremum of metric is approached (A), and gradual synchronization is performed (B). 90
Fig. 5.9. Synchronization under rapidly shifting carriers λ=7.974 (A), and slowly shifting carriers λ=8.0065 (B). 91
Fig. 5.10. Output Voltage and Current (A), LFHPI inverter side current ripples (B) in 30 kW 3P3W GC HbFPIS with common dc source. 92
Fig. 5.11. Measured LFHPI and HFLPI inverter side inductor currents, and their sum without (A) and with (B) ripple attenuation. 93
Fig. 5.12. Measured LFHPI and HFLPI inverter side inductor currents, and their sum without (A) and with (B) ripple attenuation. 93
Fig. 5.13. Measured grid currents and capacitor voltage (A) without (iTHD=5.78%) and (B) with (iTHD=4.27%) ripple compensation. 94
Fig. 5.14. Measured LFHPI and HFLPI inverter side inductor currents, and their sum without (A) and with (B) ripple attenuation. 94
Fig. 5.15. Measured grid currents and capacitor voltage (A) without (iTHD=5.44%) and (B) with (iTHD=3.94%) ripple compensation. 95
Fig. 5.16. Transient of initial synchronization (A), and persistent synchronization over half line-cycle (B). 96
Fig. 5.17. Step-up and -down experiment. 97
Fig. 5.18. Mode transition experiment. 97
Fig. 5.19. Step-up and -down experiment. 98
Fig. 5.20. Mode transition experiment. 98

 
LIST OF TABLES
Table 1.1. PRICE AND VOLUME COMPARISON TABLE BETWEEN CLASSIC AND PROPOSED INVERTER 8
Table 2.1. ACTIVE VOLTAGE VECTORS AND MOMENTS OF SWITCHING BETWEEN THEM VS. SORTED ESTIMATED DUTIES 24
Table 2.2. DC-VOLTAGE TERMS VS. VOLTAGE VECTOR 27
Table 3.1. 3P3W HbFPIS SPECIFICATIONS AND FILTER DESIGN 64
Table 3.2. SYSTEM SPECIFICATIONS AND FILTER DESIGN 65
Table 4.1. SYSTEM SPECIFICATIONS AND FILTER DESIGN 67
Table 4.2. SYSTEM SPECIFICATIONS AND FILTER DESIGN 73
Table 5.1. SYSTEM SPECIFICATIONS AND FILTER DESIGN OF 3P3W HBFPIS 80
Table 5.2. SYSTEM SPECIFICATIONS AND FILTER DESIGN OF 3P4W HBFPIS 81

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