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3-L DC Link ML Converter Properties 75 The individual gradients per phase are: s dI ( s ) I 2I NPx x outx outx x < 0 → = = (65) dsCM U DC 2 U DC s x dI ( s ) I 2I NPx x outx outx > 0 → = − = − (66) dsCM U DC 2 U DC Using (63), (64), (65), and (66) we get: s s dI I NP _ tot 4 out _ x x < 0 ∧ s y > 0 ∧ sz > 0 → = (67) dsCM U DC dI I NP _ tot 4 out _ z x < 0 ∧ s y < 0 ∧ sz > 0 → = − (68) dsCM U DC The gradient in the NP current function is always defined by the current in the phase with the unique sign in the average switching function. The two gradients in the middle section may have the same sign or a different sign, which means the function may be monotonic or non monotonic, depending on operating point. An analysis of all possible operating points shows that nonmonotonic behavior occurs for low cos(ϕ). This function can be determined for every operating point with any given voltage and current vector. The function is dynamically changing with time. Accordingly, any control scheme making use of the true NP current function must either determine it online or pre-calculate all possible operating points. One example is given in Figure 62. An overview of different operating points is given in appendix 9.6. Figure 62, NP current as function of θ and CM voltage, m = 0.3, ϕ = 1.4 4.7.2 NP current characteristics as a function of m, ϕ and θ Maximum and minimum achievable NP currents are a measure for the controllability of the NP voltage. High NP currents enable a fast change (and thus control) of the NP voltage. Minimum
76 3-L DC Link ML Converter Properties and maximum NP currents can easily be determined by the known NP current function in each operating point as presented in the previous paragraph. TABLE 23, MINIMUM AND MAXIMUM NP CURRENT IN DIFFERENT OPERATION POINTS APPLYING STANDARD MODULATION SCHEMES, APPLIES TO ALL TYPE OF 3-L DC LINK CONVERTERS cos(ϕ)=1 cos(ϕ)=0.81 (inductive) cos(ϕ)=0 (inductive) I NP-min m * 2 3 θ m * 2 3 θ m * 2 3 θ I NP-max m * 2 3 θ m * 2 3 θ m * 2 3 θ Appendix 9.5.1 gives an overview of maximum and minimum NP currents in different operating points. 4.7.3 Zero average NP current areas in function of CM Zero NP current operation is desirable to keep the low frequency NP voltage ripple as low as possible. Limits of the zero average NP current can easily be determined from the NP current function. If the NP current function crosses the zero line within the allowable operating range of the CM voltage (e.g. as in Figure 61), zero neutral point current operation is possible in the given operating point with the appropriate CM voltage. If it does not cross the zero line, zero NP current is not possible. Figure 63 shows the zero average NP current limits for a variety of load angles.
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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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Page 110 and 111: NP Control with Carrier based PWM 8
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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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