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ML Converter Topologies 39 3.7.4.1 Flying capacitor energy for MC based converters All capacitors within one MC structure are operated with the same duty cycle and all capacitors may have the same absolute voltage ripple (independently of their voltage rating), which means the relative ripple decreases with increasing voltage. This is required to avoid over voltages on the switches of the individual cells. Consequently, all capacitors require the same capacitance C 0. In the case of the MC converter with interleaved operation, the following basic equations apply to all flying capacitors: I FC ∆U = C * FC 0 (8) ∆tFC U ∆t DC FC _ max ∆ U FC _ max = k1 = I FC _ max (9) N C 0 With k 1 indicating the allowable maximum ripple ratio in function of the supply voltage and 1/N. tFC _ max = k2T SP ∆ (10) With T SP as switching period time and k 2 indicating the maximum capacitor application time ratio in function of the switching period. C ∆t I Nk T I FC _ max Nk2 = (11) k U f FC _ max FC _ max 2 SP 0 I FC _ max = = ∆U FC _ max k1U DC 1 DC sw All parameters determining C 0 are either given from the system (I, N, U DC) or can be chosen as operation parameter (k 1, f sw); k 2 depends on the topology. It indicates the largest expected application time ratio of the capacitor before current reversal in the capacitor is possible. The following graph illustrates the maximum capacitor application time ratio in an MC converter. Flying capacitors are charged or discharged by the corresponding output current, whenever the two adjacent cells do not have the same state. The current bypasses the flying capacitor when the two adjacent cells have the same state (either low or high). Figure 36 shows the example of a 4 cell MC converters with 4 carriers with regular phase shifts (π/2 between adjacent cells) and 5 sample references. For a given reference, the maximum capacitor application time corresponds with the phase shift between adjacent carriers, which is indicated with the bold sections of the reference lines. It can be seen from the figure that the capacitor application time is constant in the intermediate part of reference and going linearly to zero towards the upper and lower limits. The sign of the current in the flying capacitor can be chosen every time a state using a flying capacitor is applied.
40 ML Converter Topologies 1 0.75 0.5 0.25 Carrier 1 Carrier 2 Carrier 3 Carrier 4 Reference 1 Reference 2 Reference 3 Reference 4 Reference 5 0 0 0.25 0.5 0.75 1 Figure 36, Carrier waveform, sample reference inputs and resulting flying capacitor application times Flying capacitor application time ratio (k 2) 1 1/M 0 0 1/M (M-1)/M M Reference Figure 37, flying capacitor application time Figure 37 indicates that there is a maximum k 2 of 1/M, M indicating the number of cells that can be operated interleaved. This can correspond with the number of cells within a given MC converter, or it can be a higher number based on series connected MC’s or a combination of MC and FS cells. This number M does not necessarily correspond with N for all topologies. N is the ratio of input supply voltage of the converter over one output voltage level (or lowest capacitor voltage), whereas M can refer to only a portion of the whole converter. In the case of the MC converter N equals M; in the case of the SMC or the ANPC1 and ANPC2, N equals 2 times M. The switching frequency may also vary depending on topology and operating point. A factor k f_sw shall be defined to express the actual switching frequency in function of a base frequency corresponding with a pure MC converter operation. Starting from Figure 37, the total flying capacitor energy of all considered topologies can be calculated.
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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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Page 22 and 23: Introduction 1 2 INTRODUCTION This
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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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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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