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3-L DC Link ML Converter Properties 83 fundamental in the rectified switching function. This fundamental is phase shifted by π/2 compared to the one generated by DC CM injection. 4.8.3 Relationship between harmonic orders of input current and switching function The preceding two paragraphs have pointed out the quantitative relationship between switching function harmonics and rectified switching function harmonics. This information can now be related to the input current harmonics. As the input current needs to be multiplied with the rectified switching function as shown in (45), there is a convolution in the frequency domain. S I _ NP _ x( I _ out _ x rect _ x ω) = S ( ω) • S ( ω) (75) Accordingly, a qualitative relationship matrix can be established. TABLE 27, RELATIONSHIP BETWEEN HARMONIC ORDERS OF LINE SIDE CURRENT, THE RECTIFIED SWITCHING AND THE NP CURRENT PER PHASE Harmonic order of I NP_x Harmonic order of I out_x DC 1 2 3 4 5 6 7 8 9 DC DC 1 2 3 4 5 6 7 8 9 1 1 DC 1 2 3 4 5 6 7 8 2 2 1 DC 1 2 3 4 5 6 7 3 3 2 1 DC 1 2 3 4 5 6 4 4 3 2 1 DC 1 2 3 4 5 5 5 4 3 2 1 DC 1 2 3 4 6 6 5 4 3 2 1 DC 1 2 3 7 7 6 5 4 3 2 1 DC 1 2 8 8 7 6 5 4 3 2 1 DC 1 9 9 8 7 6 5 4 3 2 1 DC abs(s x(t)) The rectified switching function abs(s x(t)) has normally predominantly even terms, based on the fundamental and the 3 rd harmonic in the switching function s x(t), as shown in TABLE 26 in the previous paragraph. In steady state operation without DC offset or additional harmonics and pure sinusoidal input current, this will generate all odd harmonics in the NP current, including a fundamental term.
84 3-L DC Link ML Converter Properties A similar table as above can be drawn based on the actual switching function s x(t) instead of abs(s x(t)). However, such a table includes much more components, as all the harmonic terms in abs(s x(t)) can be generated by multiple terms in s x(t). TABLE 28 includes the most important components only; in reality an infinite number of higher harmonic terms apply to each field, with decreasing importance. All positive and negative sequence NP currents will cancel out in the neutral point, if the system is symmetrical and balanced. The remaining harmonics visible in the NP current and consequently in the NP voltage are 3 rd , 9 th , 15 th etc. Therefore only zero sequence NP currents are shown in TABLE 28. On the line side only positive and negative sequence currents are considered, as zero sequence currents are not present in three wire systems. TABLE 28, RELATIONSHIP BETWEEN HARMONIC ORDERS OF LINE SIDE CURRENT, THE SWITCHING FUNCTION S(T) AND THE OVERALL NP CURRENT I-NP AC side current DC 1 2 3 4 5 6 7 8 9 DC 1 DC / 2 nd / 6 th 1 st / 3 rd 4 th / 6 th 7 th / 9 th 2 1 st / 3 rd DC / 2 nd / 6 th 3 rd / 5 th 6 th / 8 th 3 4 3 rd / 5 th DC / 2 nd / 6 th 1 st / 3 rd 4 th / 6 th 5 4 th / 6 th 1 st / 3 rd DC / 2 nd / 6 th 3 rd / 5 th 6 7 6 th / 8 th 3 rd / 5 th DC / 2 nd / 6 th 1 st / 3 rd 8 7 th / 9 th 4 th / 6 th 1 st / 3 rd DC / 2 nd / 6 th 9 s(t) This overview helps to understand both how the NP can be disturbed and how it can be controlled. The input ideally only contains a fundamental and high order harmonics generated by the switching function as it is actively controlled. In reality, the input voltage (line voltage or motor back EMF) may contain low order harmonics also generating input current harmonics if not actively eliminated. These harmonics are typically odd harmonics. The convolution of input current and rectified switching function then leads primarily to odd NP current harmonics, as the rectified switching function contains primarily even harmonics (see TABLE 27). This is not very significant as there is no DC and amplitudes are low. If however there are odd harmonics in the rectified switching function, a DC NP current can be generated. If there are even harmonics present (2 nd , 4 th , etc.) in the output current, they interact with the fundamental and the 3 rd of the switching function and result in a DC NP current. To control the NP, it is best to focus on a scheme using the fundamental input current, as the presence of current harmonics is uncertain. This means that mainly a fundamental in the rectified switching function can be used to generate a DC NP current. A fundamental in the rectified switching function can be obtained by applying a DC offset or an even harmonic term to the
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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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NP Control with Optimal Sequence SV
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Application and Verification 149 7
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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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