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NP Control with Carrier based PWM 89 5 NP CONTROL WITH CARRIER BASED PWM This chapter introduces several new carrier based PWM schemes for improved NP and FC voltage control. The first two modulation schemes proposed use CM voltage injection only and can be applied to any 3-L DC link converter including the NPC. Knowledge of the NP current as a function of CM voltage is used in real-time to control the NP point. The first scheme proposed operates purely in time domain and injects a CM voltage based on instantaneous values. The second scheme makes use of harmonic relationships presented in chapter 4 and injects specific harmonics in the CM voltage. Both schemes offer the same NP current control capability as some SVM schemes proposed in literature. However, they offer a high degree of freedom regarding the base modulation type and thus allow including additional objectives like THD minimization (as for example optimized CB PWM schemes like CSPD PWM can be used) or switching loss minimization. The carrier based schemes presented in the second part of the chapter are topology specific, as they make use of redundant states. Carrier waveforms are designed such that specific redundant states are combined. Solutions for very efficient NP control are proposed for the SMC and the ANPC type 3. The NP control capacity of these schemes is significantly beyond the capacity of standard schemes only utilizing CM voltage. 5.1 Real time NP current function control scheme This scheme can be used for all 3-L DC link topologies. 5.1.1 Background The neutral point in 3-L based (input) converter systems can be controlled by a CM voltage injection. In the case of active power, a DC common mode voltage will generate a DC NP current (with superimposed AC currents at various frequencies). This allows to implement relatively simple control schemes (although the exact relationship of common mode voltage with NP current is relatively complex) to control the NP voltage. In the case of reactive power, a DC common mode voltage will generate an AC NP current (at various frequencies), so the same control schemes as for active power cannot be applied anymore. In other words, unconstrained linear feedback control with DC CM injection based on a linear approximation of the NP current function works fine for a wide operating range but delivers poor results for low cos(ϕ). This is obvious when looking at the sample NP current function in Figure 64. The endpoints provide very low NP current and the useful range (between min. and max.) of the NP function is much smaller than the physically available range. If a single linearized function is used for feedback, the result may even be counter productive as the real non-monotonic function is changing its sign of the gradient. However, as Figure 64 indicates, a suitable CM injection based on the instantaneous characteristics of the function will generate a useful NP current.
90 NP Control with Carrier based PWM Real time NP current function NP current 1.00 0.50 0.00 -0.50 INP-std Range Maximum Minimum -1.00 -1 -0.5 0 0.5 1 sCM Figure 64, NP current function for m = 0.61, ϕ = 1.51, θ = 1.7 5.1.2 Definition of the NP control scheme Only the linear sections of the NP current function between minimum and maximum NP current shall be considered. All CM values outside of those sections do not add to controllability but either keep the resulting NP current constant or even reduce the control performance (see Figure 64). The resulting function to be used for the feedback controller is always monotonic and consist of either one or two linear sections. As can be seen from the example in Figure 62, the NP current function can change significantly over time. In non monotonic functions, the peak changes its direction, pointing up and down in alternation (see the two sample functions in red and purple). The maximum or minimum point of the NP current function may jump several times within one fundamental period (once per 60° segment, e.g. Figure 65, the CM for the maximum NP current [green dot] obviously changes from minimum CM to maximum CM and the gradient of the NP current function is changing its sign). Those jumps are not desirable, as the average switching frequency on the device level is increased and losses rise. An alternate approach using harmonic CM injection, which results in a more smooth CM operation, is proposed in the next section. Real time NP current function Real time NP current function NP current 1.00 0.50 0.00 -0.50 INP-std Range Maximum Minimum NP current 1.00 0.50 0.00 -0.50 INP-std Range Maximum Minimum -1.00 -1 -0.5 0 0.5 1 sCM -1.00 -1 -0.5 0 0.5 1 sCM (a) (b) Figure 65, Real time NP current function for a given load angle (ϕ = 1.51) and modulation depth (m = 0.87) for increasing angle θ during the fundamental period (a: θ = 0.4, b: θ = 0.8)
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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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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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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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