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NP Control with Carrier based PWM 97 TABLE 32, CM VOLTAGE AND RESULTING NP CURRENT IN FUNCTION OF TIME WITH DIFFERENT LEVELS OF 6 TH HARMONIC INJECTION, REACTIVE POWER OPERATION, MODERATE MODULATIN INDEX Fundamental = 0.45*2/sqrt(3) 3 rd harmonic = 0.167 6 th harmonic = 0 Fundamental = 0.45*2/sqrt(3) 3 rd harmonic = 0.167 6 th harmonic = 0.2 Fundamental = 0.45*2/sqrt(3) 3 rd harmonic = 0.167 6 th harmonic = 2 U CM U CM U CM
98 NP Control with Carrier based PWM For low modulation depth and cos(ϕ) not equal to zero, both outer sections of the piecewise linear function have the same absolute value but opposite signs. Maximum and minimum current functions (with lowest absolute value CM) are clearly defined. These maximum and minimum current functions have singularities with CM jumps as can be seen from TABLE 34. Nevertheless, continuous CM voltage operation is possible with suitable 3 rd harmonic injection, as proposed in TABLE 34. The third harmonic required has significantly different amplitude and phase angle than the one use in TABLE 32. Of course, other strategies of CM injection staying within the minimum and maximum boundaries are possible, but a strategy leading to continuous CM injection function is preferable for commutation reasons; any jump in the CM function will generate multiple commutations simultaneously and lead to higher overall switching losses. Note that minimum and maximum NP current CM values do not cross each other in this case (as opposed to the approach in TABLE 32). Consequently, no AC CM needs to be injected to generate a DC NP current, but a pure DC CM voltage injection can be used both for minimum and maximum DC NP current. This is shown in the third column TABLE 34. Note that there is a smooth transition possible from active to reactive power with this control scheme. The 3 rd harmonic amplitude and phase can be defined as a continuous function of amplitude of the fundamental and the angle ϕ between voltage and current. The 6 th harmonic injection scheme can still be applied at low modulation depth and non zero cos(ϕ) if the CM function for minimum and maximum NP current are adapted accordingly, conforming with the constraints above. In fact the examples in TABLE 32 use a phase angle of 1.56, which leads to small but noticeable difference of NP currents in the two outer sections of the NP current functions. The performance impact is very low. Both schemes have very similar performance. The 6 th harmonic injection scheme will have slightly reduced maximum and minimum NP currents but it has a higher degree of freedom regarding 3 rd harmonic injection and it requires no DC CM injection for the NP control. We can conclude that there are two almost equivalent concepts for NP current control for reactive power operation at low modulation depth. This is not true for high modulation depth, because the outer sections of the piecewise linear CM current function cannot physically be reached. Consequently, the minimum and maximum NP current functions are clearly defined. Only 6 th harmonic injection is possible as shown in TABLE 33.
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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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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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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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