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                                                            Power electronic control in electrical systems 325

                        Using the principle of harmonic reduction, the input and output of n basic six-pulse
                      inverters (which are operated with appropriate relative phase-displacements) can be
                      combined so as to obtain an overall P ˆ 6n multipulse structure. The frequencies of
                      the harmonics present in the output voltage and input current of this P-pulse inverter
                      are [Pk   1] f and Pkf, respectively. As can be seen, the harmonic spectrum improves
                      rapidly with increasing pulse number. In addition, the amplitude of these harmonics
                      is inversely related to the pulse number; that is, the amplitude of the k-th harmonic of
                      the output voltage waveform is proportional to 1/[Pk   1] and that of the DC supply
                      current to 1/Pk (Gyugyi, 1994).
                        Consequently, the FACTS STATCOM uses many six-pulse VSCs, appropriately
                      phase shifted, with their output combined electromagnetically to produce a nearly
                      sinusoidal resultant waveform. The pulse number of such an arrangement is generally
                      quoted as six times the number of basic inverters used, and provides an indication
                      of the level of harmonic reduction achieved. For transmission line applications, a
                      pulse number of 24 or higher is required to achieve adequate waveform quality
                      without large passive filters. A single line diagram of a STATCOM system is shown
                      in Figure 8.41. The VSC combines eight three-phase inverters into a 48-pulse












































                      Fig. 8.41 Single-line diagram ofa 48-pulse VSC-based STATCOM.
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