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NP Control with Carrier based PWM 101 modulation depth and load angle cos(ϕ) to determine the transition points to switch over from one scheme to another, which is illustrated in Figure 67. DC CM injection (with limitation to maximum NP current CM values as indicated in TABLE 33) is very effective over a very large range of operation, including reactive power at low modulation depth. However, it has very poor performance for pure reactive power at high modulation depth, which is pointed out by the zoom in Figure 67. In this region, clearly 6 th harmonic injection performs better. (a) (b) Figure 67, Maximum obtainable NP currents, a) DC CM injection, b) 6 th harmonic injection To determine the transition point, the two graphs have been combined into one (Figure 68 b). The area improved by the 6 th harmonic injection is rather small. However, this is the area where STATCOM’s are operating: high modulation index and very low cos(ϕ). The performance improvement is very significant in this case. This even holds true for pure reactive power and highest physically possible modulation index. (a) (b) Figure 68, maximum obtainable NP currents, a) optimal CM injection based on true real time NP current function, b) constrained DC and 6 th harmonic injection
102 NP Control with Carrier based PWM Analytical calculation results in ~1% DC NP current for the case of cos(ϕ)=0 and m=1. This still is sufficient if there is no large bias current in the NP. For comparison, a graph with optimized, constrained CM injection based on the real time NP current function is shown in Figure 68 (a). This approach provides the highest possible NP current based on standard modulation schemes. The difference to the combined DC and 6 th harmonic injection approach is very small, indicating that this latter approach can be used without any significant loss in performance. The major difference is in handling the discontinuity of the NP current function. When using the real time NP current function alone, the minimum NP current value is jumping form one side to the other at some point and the gradient of the function is changing abruptly (Figure 65). This leads to a CM jump that either generates additional losses or needs to be limited with a given rate of change. The 6 th harmonic injection on the other hand also leads to a zero crossing in that point, however automatically limits the rate of change by its sinusoidal waveform. With increasing gain, almost the same peak NP current can be obtained. The NP control schemes “real time NP current function” and “6 th harmonic injection” are therefore equivalent. 5.2.2 6 th harmonic injection based NP control implementation The 6 th harmonic injection scheme has been integrated in a PD PWM as introduced in chapter 4. The actual 6 th harmonic controller is only active in the area indicated with a red border line in Figure 68 in the zoomed area. Outside of that area, a DC CM injection is used. A pure proportional feedback is considered sufficient for this application. TABLE 35, OPERATING POINT FOR EXPERIMENTAL VERIFICATION OF REAL TIME NP CURRENT SCHEME AND 6 TH HARMONIC INJECTION SCHEME m f out U DC U FC R load L load ϕ UI C DC C FC f sw 0.75 50 Hz 240 V 60 V 0.5 Ω 14.2 mH 1.53 990µF 1120µF 2000 Hz (a) (b) (c) CH1 (yellow): U out1 CH2 (cyan): U out2 CH3 (magenta): U NP CH4 (green): I out2 MATH (red): U out1-2 Figure 69, Steady state operation with reactive load and two different NP control schemes applied: Real time NP current function m = 0.75 (a), 6 th harmonic injection with m = 0.75 (b), 6 th harmonic injection with step form 0.2 to 0.9
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THÈSE En vue de l'obtention du DOC
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Acknowledgements i ACKNOWLEDGEMENTS
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iv Table of Contents 3.4 Generic ML
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vi Table of Contents 7.1 General mo
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viii Résumé français (French sum
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x Résumé français (French summar
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xii Résumé français (French summ
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xiv Résumé français (French summ
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xvi Résumé français (French summ
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xviii Résumé français (French su
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Introduction 1 2 INTRODUCTION This
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Introduction 3 tighter capacitor di
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Introduction 5 TABLE 1, OPERATING R
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Introduction 7 2.3 Glossary Note th
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Introduction 9 2.4 Nomenclature Not
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Introduction 11 DPC DSP DTC FC FPGA
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ML Converter Topologies 13 3 ML CON
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ML Converter Topologies 15 The four
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ML Converter Topologies 17 Each swi
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ML Converter Topologies 19 size doe
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ML Converter Topologies 21 plus (a)
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ML Converter Topologies 23 N >= 2,
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ML Converter Topologies 25 (a) (b)
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ML Converter Topologies 27 (a) (b)
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ML Converter Topologies 29 In a pra
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ML Converter Topologies 31 reality,
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ML Converter Topologies 33 All cons
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ML Converter Topologies 35 TABLE 16
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ML Converter Topologies 37 TABLE 17
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ML Converter Topologies 39 3.7.4.1
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ML Converter Topologies 41 f C sw =
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ML Converter Topologies 43 A second
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ML Converter Topologies 45 Limitati
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ML Converter Topologies 47 1 K M 2
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ML Converter Topologies 49 3.8 Exec
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Application and Verification 151 TA
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Application and Verification 153 Th
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Application and Verification 155 7.
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170 Conclusions and Outlook 8.1.2 M
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172 Conclusions and Outlook 8.2 Out
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174 Conclusions and Outlook 8.3 Sum
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176 Appendix I = 1− ) (99) ( C 2
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178 Appendix TABLE 78, FLYING CAPAC
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180 Appendix 9.3 Single phase NP cu
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182 Appendix 9.4 States of the ANPC
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184 Appendix 9.5 NP currents as a f
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186 Appendix 9.5.3 Maximum and mini
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188 Appendix 9.6 NP current functio
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190 Appendix TABLE 91, NP CURRENT I
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192 Appendix TABLE 93, NP CURRENT I
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Bibliography 195 10 BIBLIOGRAPHY [1
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Bibliography 197 [33] P. Steimer,
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Bibliography 199 neutral point bala
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Bibliography 201 [88] J. Pou, J. Za
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Christoph Haederli - Les thÃ¨ses en ligne de l'INP - Institut National ...

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