Title Page
Abstract
Contents
Abbreviations 17
Chapter 1. Introduction 18
1.1. DC Microgrid 18
1.2. Control Principle in DC Microgrids 20
1.2.1. Local Control Level in DC Microgrids 21
1.2.2. Secondary Control Level in DC Microgrids 24
1.2.3. Communication Time Delays in Distributed Control Scheme 26
1.3. Objectives of the Thesis 30
1.4. Contribution of the Thesis 31
1.5. Outline of the Thesis 32
Chapter 2. Double Secondary Controllers Against Heterogeneous Communication Time Delays 34
2.1. Control Scheme to Overcome Heterogeneous Time Delays 35
2.1.1. Weighted Average Estimator based on PI Consensus Algorithm and Scattering Transformation 35
2.1.2. Proposed Control Scheme 39
2.2. Stability Analysis 41
2.3. Simulation Results 43
2.4. Experiment Results 53
2.5. Conclusion of the Chapter 62
Chapter 3. Single Secondary Controller Against Heterogeneous Communication Time Delays 63
3.1. Preliminaries 64
3.1.1. Secondary Control Scheme for Voltage Restoration and Power Sharing and Their Limitations. 64
3.1.2. Conventional Consensus-Based Estimator and Their Limitations 65
3.2. Proposed Distributed Control Scheme against Heterogeneous Time Delays 66
3.3. Stability Analysis 69
3.4. Simulation Results 73
3.4.1. Estimated Average 75
3.4.2. Uncertain Time Delays and Intermittent Change in Time Delays 77
3.4.3. Cancellation of Nonzero Initial Condition 82
3.4.4. Accurate Power Sharing and Voltage Restoration 83
3.5. Experiment Results 84
3.5.1. Estimated Average 86
3.5.2. Uncertain Time Delays and Intermittent Change in Time Delays 87
3.5.3. Cancellation of Nonzero Initial Condition 88
3.5.4. Accurate Power Sharing and Voltage Restoration 90
3.6. Conclusion of the Chapter 91
Chapter 4. Conclusions and Future Works 93
4.1. Conclusions 93
4.2. Future Works 94
Appendix A. Proof of Lemma 2 96
Bibliography 100
Publications 110
TABLE 2.1. SYSTEM PARAMETERS 44
TABLE 2.2. TIME DELAYS FOR THREE CASES 46
TABLE 3.1. SYSTEM PARAMETERS 74
TABLE 3.2. Heterogeneous Time Delays In Three Cases With Different Ts[이미지참조] 74
TABLE 3.3. THREE CASES OF UNCERTAIN TIME DELAYS 80
Figure 1.1. Renewable power generation by country or region in 2017. 18
Figure 1.2. A typical DC microgrid. 19
Figure 1.3. Local control level with current, voltage, and droop loops. 21
Figure 1.4. Simplified local control level by two DGs. 22
Figure 1.5. Current-based droop and power-based droop. 23
Figure 1.6. DC microgrid with line resistances. 23
Figure 1.7. Secondary control strategy. 24
Figure 1.8. Centralized control scheme. 25
Figure 1.9. Distributed control scheme. 26
Figure 1.10. Consensus-based distributed control scheme. 27
Figure 1.11. Communication network topology with 6 DG units. 27
Figure 1.12. Error produced by heterogeneous time delays (a) homogeneous time delay and (b) heterogeneous time delays. 30
Figure 2.1. Proposed control scheme. 40
Figure 2.2. Closed loop pole movement when increasing integration gain kip of accurate power sharing controller from 0.035 to 40.[이미지참조] 43
Figure 2.3. Closed loop pole movement when increasing integration gain kiv of voltage restoration controller from 1 to 10.[이미지참조] 43
Figure 2.4. Structure of DC MG used for simulation and experiment. 44
Figure 2.5. Line communication graph. 44
Figure 2.6. The i-th controller updates the estimator with fixed sampling time Ts_est.[이미지참조] 45
Figure 2.7. Asynchronous operation of local controllers and time delay, τij, τji.[이미지참조] 45
Figure 2.8. Heterogeneous time delays with three controllers. 45
Figure 2.9. Average voltage and estimated average voltage based on conventional consensus algorithm: (a) Case 1 (b) Case 2 and (c) Case 3. 47
Figure 2.10. Average voltage and estimated average voltage based on the proposed estimator: (a) Case 1 (b) Case 2 and (c) Case 3. 48
Figure 2.11. Average voltage and estimated average voltage based on the proposed estimator under switching load condition: (a) Case 1 (b) Case 2 and (c) Case 3. 49
Figure 2.12. Average power per unit and estimated average power per unit based on the proposed estimator under switching load condition: (a) Case 1 (b) Case 2 and (c) Case 3. 50
Figure 2.13. Voltage restoration in (a) Case 1 (b) Case 2 and (c) Case 3. 51
Figure 2.14. Accurate power sharing in (a) Case 1 (b) Case 2 and (c) Case 3. 51
Figure 2.15. Output voltage response under change of kip: (a) kip=0.035; (b) kip=1; (c) kip=10; (d) kip=100.[이미지참조] 52
Figure 2.16. Output voltage response under change of kiv: (a) kiv=1; (b) kiv=5; (c) kiv=8; (d) kiv=12.[이미지참조] 53
Figure 2.17. DC microgrid in laboratory. 54
Figure 2.18. CAN bus implementation. 54
Figure 2.19. Communication among three DSPs in the experiment. 55
Figure 2.20. Average voltage estimation based on conventional consensus algorithm: (a) Case 1, (b) Case 2 and (c) Case 3. 55
Figure 2.21. Average voltage estimation based on proposed estimator: (a) Case 1, (b) Case 2 and (c) Case 3. 56
Figure 2.22. Average voltage and estimated average voltage of proposed estimator under switching load condition: (a) Case 1, (b) Case 2 and (c) Case 3. 57
Figure 2.23. Average power per unit and estimated average power per unit of proposed estimator under switching load condition: (a) Case 1, (b) Case 2 and (c) Case 3. 58
Figure 2.24. Voltage restoration with proposed control scheme: (a) Case 1, (b) Case 2 and (c) Case 3. 59
Figure 2.25. Accurate power sharing with proposed control scheme: (a) Case 1, (b) Case 2 and (c) Case 3. 59
Figure 2.26. Output voltage response under change of kip: (a) kip=0.035; (b) kip=1; (c) kip=10; (d) kip=100.[이미지참조] 60
Figure 2.27. Output voltage response under change of kiv: (a) kiv=1; (b) kiv=5; (c) kiv=8; (d) kiv=12.[이미지참조] 61
Figure 3.1. Two secondary controllers in conventional voltage shifting method. 64
Figure 3.2. Proposed control scheme. 67
Figure 3.3. Movement of system poles when increasing ksp of secondary controller from 0.01 to 1.0.[이미지참조] 72
Figure 3.4. Movement of system poles when increasing ksi of secondary controller from 1 to 100.[이미지참조] 72
Figure 3.5. Configuration of the DC MG in laboratory. 73
Figure 3.6. Line topology. 73
Figure 3.7. The estimator is updated at time instants tki, tk+1i, tk+2i... with fixed sampling time Ts.[이미지참조] 75
Figure 3.8. The time delays tij and tji.[이미지참조] 75
Figure 3.9. The performance of conventional estimator in Case 1, Case 2, and Case 3. 76
Figure 3.10. The performance of proposed estimator in Case 1, Case 2, and Case 3. 77
Figure 3.11. The performance of proposed estimator with load variation in Case 1, Case 2, and Case 3. 78
Figure 3.12. Three cases Case 4, Case 5, and Case 6 in which three controllers update the proposed estimator. 79
Figure 3.13. Uncertain time delay performance with the proposed estimator in Case 4, Case 5, and Case 6. 80
Figure 3.14. Intermittent change in time delays with the proposed estimator. 81
Figure 3.15. Cancellation of nonzero initial condition with the proposed estimator. 81
Figure 3.16. Power allocation performance in Case 1, Case 2, and Case 3. 82
Figure 3.17. Voltage restoration performance in Case 1, Case 2, and Case 3. 83
Figure 3.18. DC microgrid in experiment. 84
Figure 3.19. CAN bus in experiment. 84
Figure 3.20. Estimation performance by using conventional consensus-based estimator in Case 1, Case 2, and Case 3. 85
Figure 3.21. Estimation performance of the proposed estimator in Case 1, Case 2, and Case 3. 86
Figure 3.22. Estimation performance of the proposed estimator with load variation in Case 1, Case 2, and Case 3. 87
Figure 3.23. Performance of the proposed estimator under uncertain time delays. 88
Figure 3.24. Average lambda estimation by using the proposed estimator under intermittent change in time delays. 89
Figure 3.25. Cancellation of nonzero initial condition with the proposed estimator: a) x ₁(0)=5, x₂(0)=10, x₃(0)=15 and b) x₁(0)=4, x₂(0)=1, x₃(0)=12. 89
Figure 3.26. Accurate power sharing by using proposed method in Case1, Case 2, and Case 3. 90
Figure 3.27. Voltage restoration performance in Case1, Case 2, and Case 3. 91