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ML Converter Topologies 41 f C sw = k f (12) I f _ sw * NT sw _ base I N I FC _ max SP FC _ max FC _ max 0 = = = (13) Mk1U DC Mk1U DC fsw Mk1U DC f sw _ basek f _ sw I FC _ max IFC _ maxN Mk f _ sw Mk f _ sw C1 = = = C0 (14) k U f Mk U f N N 1 DC sw _ base 1 DC sw N C = 0 C1 (15) Mk f _ sw N C 0 refers to the actual capacitance required, taking into account the level over interleaving and the applied switching frequency. C 1 is a generic value depending on maximum current, maximum voltage ripple and base switching frequency. It can be seen from (15) that a reduction of the number of cells can be compensated with higher switching frequency. With a total number of k flying capacitors, we get the total energy in the flying capacitors: E tot = k ∑ x= 1 C0U 2 2 x = k ∑ C1NU 2Mk 2 x x= 1 f _ sw (16) A constant shall be defined as follows to compare different topologies without taking into account any absolute values from a given operating point. E tot I U 2 C1U DC FC _ max DC = K E _ cap = K E _ cap (17) 2 2k1 f sw _ base (18) follows directly from (16) and (17). 2 k 2E ⎛ ⎞ tot N U x K _ = = 2 ∑ ⎜ ⎟ E cap (18) C1U Mk DC f _ sw x= 1 ⎝U DC ⎠ In the case of p groups of flying capacitors with each group forming a MC, this can also be written as (k/p is the number of flying capacitors per group): ∑∑ − 2 p 1 k / p N ⎛U y+ x* k / p ⎞ K E _ cap = ⎜ ⎟ (19) Mk f _ sw x= 0 y= 1 U DC ⎝ ⎠ With p identical groups of flying capacitors this results in: 2 k / p pN ⎛ U y ⎞ K _ = ∑ ⎜ ⎟ (20) E cap Mk f _ sw y= 1 ⎝U DC ⎠
42 ML Converter Topologies In a fully redundant MC converter, the voltage sequence in the capacitors is given: yU U = DC y N (21) This can be inserted in the equation above 2 k / p k / p pN ⎛ yU ⎞ DC p 2 K = ∑ ⎜ ⎟ E cap = ∑ y (22) _ Mk f _ sw y= 1 ⎝ NU DC ⎠ MNk f _ sw y= 1 3 ( k / p) ( k / p) 2 p ⎛ ⎞ ⎜ k / p K = ⎟ E _ cap + + (23) MNk f _ sw ⎝ 3 2 6 ⎠ E tot I U ⎛ 3 ( k / p) ( k / p) 2 FC _ max DC p k / p FC _ max DC = KE _ cap = ⎜ k fsw base MNk + + (24) 1 _ f _ sw 3 2 6 2k1 fsw _ base 2 ⎟ ⎝ ⎠ ⎞ I U Thanks to the parameterization, these equations can be used to calculate the total flying capacitor energy for a wide range of different topologies. The meaning of parameters shall be repeated here for clarity: TABLE 19, PARAMETER DEFINITIONS p k M N k f_sw number of identical groups of MC converters (non overlapping) total number of flying capacitors number of cells that can be operated interleaved input voltage divided by smallest capacitor voltage (number of cells in pure MC converter) switching frequency factor to get actual maximum switching frequency from maximum switching frequency that can be used in the MC converter (f sw_base) k 1 maximum allowable voltage ripple ratio ∆U/U N Depending on the given boundary conditions different parameters may be used. The following paragraphs list the resulting capacitor energies for three different operating conditions: Operational limitation by peak switching frequency of device, operational limitation by average switching frequency of device and operational limitation by apparent output switching frequency of converter. The corresponding tables are given in appendix 9.2.1. 3.7.4.1.1 Operational limitation by peak device switching frequency Operational limitation of a converter may be given by the peak device switching frequency. This limitation may be based on two different reasons. The first one being gate driving limitation, for example in the case where IGCT are used. IGCT gate drivers always have limited operating frequency, optimized according to a trade of between cost and performance in its target application.
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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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Page 22 and 23: Introduction 1 2 INTRODUCTION This
Page 24 and 25: Introduction 3 tighter capacitor di
Page 26 and 27: Introduction 5 TABLE 1, OPERATING R
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Page 32 and 33: Introduction 11 DPC DSP DTC FC FPGA
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NP Control with Carrier based PWM 9
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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 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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