分散式主動濾波系統: 一種新式電力系統諧波的解決方案

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研究生：	李宗璘 Tzung-Lin Lee
論文名稱：	分散式主動濾波系統: 一種新式電力系統諧波的解決方案 Distributed Active Filter Systems: A New Approach to Power System Harmonics
指導教授：	鄭博泰 Po-Tai Cheng
口試委員:
學位類別：	博士 Doctor
系所名稱：	電機資訊學院 - 電機工程學系 Department of Electrical Engineering
論文出版年：	2007
畢業學年度：	95
語文別：	英文
論文頁數：	122
中文關鍵詞：	分散式主動濾波系統、諧波振盪、下降控制、分散式發電系統、諧波阻尼
外文關鍵詞：	Distributed active filter systems, Harmonic resonance, Droop control, Distributed generation systems, Harmonic damping
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本論文提出分散式主動濾波系統以抑制電力系統中諧波電壓失真的問題。在這種分散式主動濾波系統中，主動濾波器是沿著配電線路安裝的，他們可以安裝在相同或不同的位置。而每一主動濾波器藉著內建的諧波電導-消耗伏安的下降控制器，使得主動濾波器操作為具有下降特性的諧波電導。下降的斜率則由主動濾波器的額定容量來決定，以確保在濾波器間沒有任何通訊傳輸下，每一濾波器所消耗的伏安能與其額定容量成正比。透過電腦模擬及實驗量測，可驗證所提出的分散式主動濾波系統可有效的運作。此外，主動濾波器的濾波效果可藉由諧波電壓駐波理論來解釋，並可由此決定分散式主動濾波系統最佳安裝位置。分析的結果顯示，在輻射型或環狀型的配電系統中，主動濾波器的安裝地點取決於其所分解的電力饋線長度是否小於主要的諧波電壓波長的一半。所以，相較於終端式主動濾波器或集中式安裝主動濾波系統，分散式安裝的主動濾波系統具有較佳的濾波效果。
所提出的諧波電導下降控制演算法也可應用於抑制分散式發電系統中的諧波電壓失真的問題。由於諧波電導-諧波虛功率的下降控制器可與實功率-頻率及基頻虛功率-電壓振幅下降控制器獨立運作，所以在沒有通訊系統下，分散式安裝的發電系統所提供的實功率、基頻虛功率及諧波虛功率與發電系統介面反流器額定容量成正比。再者，為維持電力饋線電壓品質，本文亦提出一種具有動態調整策略的分散式主動濾波系統。該主動濾波器的容量將根據連接點電壓諧波的大小做動態的調整，以期當非線性負載增加或降低時，整個饋線上具有一致的電壓品質。

This dissertation proposes a distributed active filter system (DAFS) for alleviating harmonic voltage distortion in the power system. The proposed DAFS consists of multiple active filter units (AFUs) installed on the same location or various locations along the power line. A droop relationship between the harmonic conductance command and the volt-ampere consumption is developed and programmed into the controller of each unit so that each individual AFU operates as a harmonic conductance with droop characteristic. The slope of the droop is determined by the volt-ampere rating of the AFU to assure even distribution of filtering workload in proportion to the rated capacity of each unit without any communications. Test results based on computer simulations and experiments validate the effectiveness of the proposed approach. In addition, the filtering performance is discussed based on harmonic voltage standing waves to determine suitable AFU
installation location. Breaking the feeder into several segments smaller than half wavelength of dominant harmonic
frequencies is a key strategy to deploy AFUs whether in a radial line or a loop line. Therefore, distributed installation active filters provide effective filtering approach compared with termination installation or concentration installation active filters.

The proposed droop control algorithm is also effective for harmonic suppression applications in distributed generation systems. Together with real power-frequency droop and reactive power-voltage droop, each distributed generation units can provide the real power, the reactive power, and the harmonic volt-ampere reactive (var) based on their rated capacity. Furthermore, to maintain voltage quality at a desired level, the DAFS with dynamic tuning method is presented. In this algorithm, the volt-ampere capacity of the AFU is dynamically adjusted according to the voltage THD at the installation point, so that the voltage waveforms throughout the feeder are kept at a uniform level
in response to increasing or decreasing of nonlinear loads.

TABLE OF CONTENTS
Page
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Dissertation organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Passive filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Active filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Shunt active filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Series active filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.3 Hybrid active filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Harmonic resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Voltage detection active filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Termination installation active filter . . . . . . . . . . . . . . . . . . . . . 17
2.4.2 Multiple installation active filter systems . . . . . . . . . . . . . . . . . . 19
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Operational principles of the distributed active filter system . . . . . . . . . . . . . 21
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Operation principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.1 Droop controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.2 Harmonics extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.3 Current regulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Volt-ampere sharing characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.4 Design consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
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3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 Simulations and experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2.1 AFU1 and AFU2 at Bus 9 . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2.2 AFU1 at bus 9 and AFU2 at bus 4 . . . . . . . . . . . . . . . . . . . . . . 31
4.2.3 AFU1 and AFU2 of different VAratings . . . . . . . . . . . . . . . . . . . 36
4.2.4 Summary of simulation results . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3 Laboratory test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3.1 AFU1 and AFU2 of the same VA rating . . . . . . . . . . . . . . . . . . . 39
4.3.2 AFU1 and AFU2 of different VA rating . . . . . . . . . . . . . . . . . . . 42
4.3.3 Summary of experimental results . . . . . . . . . . . . . . . . . . . . . . 43
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5 Deployment strategies for distributed active filter systems . . . . . . . . . . . . . . . 46
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2 Harmonic damping analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2.1 Radial line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2.2 Loop line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.3 Simulation verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.1 Radial line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.2 Loop line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4 Experimental verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4.1 Radial line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4.2 Loop line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6 Droop-controlled harmonic filtering for distributed generation
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.1.1 Harmonic issues in distributed generation systems . . . . . . . . . . . . . 68
6.1.2 Droop-controlled harmonic filtering . . . . . . . . . . . . . . . . . . . . . 69
6.2 Operation Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2.1 Droop controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2.2 Voltage controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
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Appendix
Page
6.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.3.1 Short line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.3.2 Long line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.4 Laboratory test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7 A dynamic tuning method for distributed active filter systems . . . . . . . . . . . . 89
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.2 Operation principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.2.1 Droop controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2.2 Dynamic tuning controller . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.3.1 DAFS with the fixed droop characteristic . . . . . . . . . . . . . . . . . . 94
7.3.2 DAFS with dynamic tuning method . . . . . . . . . . . . . . . . . . . . . 97
7.3.3 Comparison of different active filter systems . . . . . . . . . . . . . . . . 98
7.4 Dynamic Analysis of the DAFS . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.4.1 Dynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.4.2 Frequency domain analysis and time domain verification . . . . . . . . . . 102
7.5 Laboratory test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.5.1 Single AFU at the end bus . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.5.2 Two AFUs in different locations . . . . . . . . . . . . . . . . . . . . . . . 108
7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
8 Conclusion and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
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LIST OF TABLES
Table Page
1.1 Voltage distortion limits in IEEE std. 519-1992 . . . . . . . . . . . . . . . . . . . . . 2
4.1 Bus voltage THDs with both AFUs installed at bus 9. . . . . . . . . . . . . . . . . . . 30
4.2 Bus voltage THDs when AFU1 at bus 9 and AFU2 at bus 4. . . . . . . . . . . . . . . 31
4.3 Transition of G, S and P of AFUs in response to load increase. . . . . . . . . . . . . 33
4.4 Bus voltage THDs with AFUs of different ratings installed at different locations. . . . 36
4.5 THDs of line voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.6 Operation of AFUs in section 4.3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.7 Operation of AFUs in section 4.3.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.1 Parameters of a given power line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2 Statistics of THDv along the radial line when AFU1 is at bus 8 and AFU2 is at various
installation locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.1 The simulation parameters of DGUs in the short line model. . . . . . . . . . . . . . . 74
6.2 Parameters of the long line circuit model. . . . . . . . . . . . . . . . . . . . . . . . . 78
6.3 The simulation parameters of DGUs in the long line model. . . . . . . . . . . . . . . 78
6.4 The Operation of distributed DGU deployment at bus 1, 5, and 10. . . . . . . . . . . . 81
6.5 The harmonic conductance command, the harmonic var, the voltage THD, and the
real power of both DGUs in Figure 6.10. . . . . . . . . . . . . . . . . . . . . . . . . 84
6.6 The operation of both DGUs in Figure 6.12. . . . . . . . . . . . . . . . . . . . . . . . 84
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Table Page
7.1 Parameters of harmonic sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.2 AFU roots before and after step load change in the fixed droop control. . . . . . . . . 104
7.3 AFU Settling time with the fixed droop control. . . . . . . . . . . . . . . . . . . . . . 105
7.4 THDs of line voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.5 The operation of single AFU at end bus. . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.6 The operation of two AFUs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
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LIST OF FIGURES
Figure Page
2.1 Circuit configurations of passive filters. . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 The typical circuit configuration of a shunt active filter. . . . . . . . . . . . . . . . . . 7
2.3 The control of shunt active filter by using p-q theory. . . . . . . . . . . . . . . . . . . 8
2.4 The circuit configuration of a series active filter. . . . . . . . . . . . . . . . . . . . . . 10
2.5 The control of the series active filter by using p-q theory. . . . . . . . . . . . . . . . . 10
2.6 The typical circuit configuration of a hybrid series active filter. . . . . . . . . . . . . . 12
2.7 SRF controller for a hybrid series active filter. . . . . . . . . . . . . . . . . . . . . . . 12
2.8 The typical circuit configuration of a hybrid shunt active filter. . . . . . . . . . . . . . 14
2.9 The control of hybrid shunt active filter by using p-q theory. . . . . . . . . . . . . . . 14
2.10 The experimental circuit, bus voltage and current waveforms for illustrating the harmonic
resonance phenomenon [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.11 Installation of voltage detection active filter. . . . . . . . . . . . . . . . . . . . . . . . 17
2.12 A termination installation active filter installed in a radial distribution feeder. . . . . . 17
2.13 Control block diagram of termination installation active filter. . . . . . . . . . . . . . 17
2.14 The adjustment scheme for harmonic conductance command. . . . . . . . . . . . . . 18
2.15 Multiple installation active filter systems with center host computer. . . . . . . . . . . 19
3.1 The proposed DAFS and the associated control. . . . . . . . . . . . . . . . . . . . . . 22
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Figure Page
3.2 A simplified circuit model at harmonic frequencies for evaluating the effectiveness of
the G − S droop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Error estimation of volt-ampere sharing in the proposed droop control. . . . . . . . . . 28
4.1 The inverter circuit of the active filter unit. . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 Simulation results of section 4.2.1: AFUs are installed at the end of the power line;
Voltage waveforms at bus 1, 2, 4, 6, 9, and active filter currents of AFU1 and AFU2. . . 32
4.3 Simulation results of section 4.2.2: AFUs are installed at different locations; Voltage
waveforms at Bus 1, 2, 4, 6, 9, and active filter currents of AFU1 and AFU2. . . . . . . 34
4.4 Transition of the AFUs operations in response to load increase. . . . . . . . . . . . . . 35
4.5 Simulation results of section 4.2.3: AFUs of different VA ratings are installed at different
locations; voltage waveforms at Bus 1, 2, 4, 6, 9, and active filter currents of
AFU1 and AFU2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.6 A laboratory test bench of the proposed DAFS. . . . . . . . . . . . . . . . . . . . . . 39
4.7 Line voltages of all 4 buses. Top to bottom: bus 1, bus 2, bus 3, and bus 4. X axis:
4ms/div; Y axis: 200V/div. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.8 Operation of the AFU’s inverter. Top to bottom: inverter reference current, inverter
output current, inverter terminal voltage. X axis: 4ms/div; Y axis: 2A/div(i) or 200V/div(Ebus). 41
4.9 G1, S1 and G2, S2 of AFUs. X axis: 4 s/div; Y axis: 0.2
−1/div(G) or 200VA/div(S). . . . . . 42
4.10 G1, S1 and G2, S2 of AFUs. X axis: 4 s/div; Y axis: 0.2
−1/div(G) or 200VA/div(S). . . . . . 43
4.11 Voltage THDs under different load and AFUs locations based on simulation. X axis:
Bus number ; Y axis: VTHD(%) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.1 The distributed-parameter model of a radial line at harmonic frequencies. . . . . . . . 48
5.2 The magnifying factor along the radial line with termination installation active filter. . 48
5.3 The magnifying factor along the radial line with AFU1 at x = 8 km and AFU2 at
x = 4 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
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Appendix
Figure Page
5.4 The average magnifying factor for various installation locations of AFU2 with different
VA capacity when AFU1 is at bus 8. . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.5 The total magnifying factor for two deployments of AFUs with different VA capacity
in the radial line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.6 The equivalent distributed-parameter model of a loop line at harmonic frequencies. . . 53
5.7 The magnifying factor along the loop line if both AFU1 and AFU2 are installed at
x = 5 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.8 The magnifying factor along the loop line if AFU1 and AFU2 are installed at x = 5 km
and x = 3 km respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.9 The total magnifying factor for various deployments of AFUs with different VA capacity
in the loop line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.10 Simulation circuits and results in the radial line. . . . . . . . . . . . . . . . . . . . . . 58
5.11 THDv along the radial line in figure 5.10(a) and figure 5.10(b) for AFUs of various
capacity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.12 Simulation circuits and results in the loop line. . . . . . . . . . . . . . . . . . . . . . 61
5.13 Experimental circuits and results in the radial line. . . . . . . . . . . . . . . . . . . . 63
5.14 Experimental circuits and results in the loop line. . . . . . . . . . . . . . . . . . . . . 65
5.15 Deployment strategies of the DAFS and the resulting pattern of harmonic voltages
(vertical axis : the amplitude of harmonic voltage standing wave, horizontal axis :
feeder location). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.1 Multiple distributed generation units in an islanding network and the control block
diagram of the proposed harmonic filtering strategy. . . . . . . . . . . . . . . . . . . 70
6.2 A short line circuit model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.3 Distributions of the real power, the reactive power, and the harmonic var in the short
line. (solid line:DGU1; dash line:DGU2) . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.4 The voltages, currents, fifth harmonic currents, and seventh harmonic currents of both
DGUs in different operation modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
x
xi
Appendix
Figure Page
6.5 Simulation results for the ratio of harmonic var consumption vs. the ratio of rated
harmonic var capacity. (∗: simulation results; solid line: theoretical value.) . . . . . . 78
6.6 A long line circuit model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.7 Voltage THD on all buses under four different DGU deployments. . . . . . . . . . . . 79
6.8 The circuit model of distributed DGU deployment at bus 1, 5, and 10. . . . . . . . . . 81
6.9 Laboratory test bench. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.10 Time response of the harmonic var, the harmonic conductance command, and the real
power for both DGUs with the same rated capacity, X axis: 10 s/div. . . . . . . . . . . 82
6.11 The operation of both DGUs during T1 < t < T2 in Figure 6.10, I:10A/div, V :100V/div. . . 83
6.12 Time response of the harmonic var and harmonic conductance command for both
DGUs with different rated capacity,H01=200 var,H02=100 var, b1=0.005V−2, b2=0.01V−2,
H1,H2:100 var/div, G1,G2:0.1
−1/V , X axis:10 s/div. . . . . . . . . . . . . . . . . . . . . . 85
6.13 A test circuit for estimating harmonic var capacity. . . . . . . . . . . . . . . . . . . . 85
6.14 Test results for voltage THD vs. harmonic var consumption of DGU under 0.09 pu,
0.18 pu, 0.36 pu, 0.72 pu, and 1.0 pu real power consumption. . . . . . . . . . . . . . 87
6.15 Test results for voltage THD vs. the ratio of harmonic var to the apparent power
delivered by the DGU under 0.09 pu, 0.18 pu, 0.36 pu, 0.72 pu, and 1.0 pu real power
consumption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.1 The DAFS with the proposed dynamic tuning method and the associated control. . . . 90
7.2 A simplified calculation block of volt-ampere consumption for AFUi. . . . . . . . . . 92
7.3 The control of the proposed dynamic tuning method. . . . . . . . . . . . . . . . . . . 93
7.4 Circuit configuration and steady-state simulation results. . . . . . . . . . . . . . . . . 95
7.5 Time response of volt-ampere consumption (kVA) and conductance command (
−1)
for both AFU1 and AFU2 when nonlinear loads increase. . . . . . . . . . . . . . . . . 96
7.6 Voltage harmonic components under no AFUs and various active filter systems . . . . 99
xi
xii
Appendix
Figure Page
7.7 AFU roots for the fixed droop control with variation of the droop coefficient (bi=0.001,
0.0025, 0.005, and 0.01) for various AFU capacity (• : Sio = 3000, × : Sio = 2500,
∗ : Sio = 2000, ◦ : Sio = 1500,⋄ : Sio = 1000). . . . . . . . . . . . . . . . . . . . . . 103
7.8 Time response when nonlinear load NLA increases at 1.5s. . . . . . . . . . . . . . . . 103
7.9 AFU complex roots for the dynamic tuning control with variation of the product of
the droop coefficient and AFU capacity (C=20, 15, 12.5, 10, 7.5, and 5). . . . . . . . . 105
7.10 Time response of conductance command of AFU2 and pole locations when nonlinear
load NLA increases at 3.0s for four different cases: case A (kp = 105,ki = 5 × 106),
case B (kp = 105,ki = 2 × 106), case C (kp = 105,ki = 1 × 106), and case D
(kp = 105,ki = 5 × 105) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.11 Time response of conductance command of AFU2 when nonlinear load NLA increases
at 3.0s for three different cases: case E (kp = 5 × 105,ki = 5 × 105), case F (kp =
105,ki = 5 × 105), and case G (kp = 104,ki = 5 × 105) . . . . . . . . . . . . . . . . . 106
7.12 Experimental circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.13 Time response of the conductance command and volt-ampere consumption of AFU1.
Y axis(G:0.2
−1/V , S:100VA/V , V:100V/V ) . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.14 Time response of AFUs in constant conductance operation mode. Y axis(G:0.2
−1/V ,
S:100VA/V , VTHD:3%/V ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.15 Time response of AFUs in the DAFS with fixed droop control. Y axis(G:0.2
−1/V ,
S:100VA/V , VTHD:3%/V ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.16 Time response of AFUs in the DAFS with the proposed dynamic tuning method. Y
axis(G:0.2
−1/V , S:100VA/V , VTHD:3%/V ) . . . . . . . . . . . . . . . . . . . . . . . . 112

                                

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