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                                                            Power electronic control in electrical systems 203



































                      Fig. 6.28 Quadrants of operation of the single-phase full-bridge VSC.

                        The fundamental component of the output voltage v o waveform has an amplitude
                      value of
                                                 ^      ^      4   V dc
                                                (V o ) ˆ (V AB ) ˆ  p                    (6:20)
                                                   1
                                                            1
                      And its various harmonics are given by
                                                           ^
                                                          (V o )
                                    ^      ^      4   V dc    1
                                  (V o ) ˆ (V AB ) ˆ  p   h  ˆ  h  h ˆ 3, 5, 7, 9, ...   (6:21)
                                               h
                                      h
                      where h is the order of the harmonic.
                        The converter is capable of operating in all four quadrants of voltage and current
                      as shown in Figure 6.28. The various modes and their relationship to the switching
                      and/or conduction state of the semiconductors are also summarized in Table 6.4 for
                      further clarity. The phase relationship between the AC output voltage and AC
                      output current does not have to be fixed and the converter can provide real and
                      reactive power at all leading and lagging power factors. However, the converter itself
                      cannot control the output voltage if the DC bus voltage V dc remains constant. There
                      is a need to adjust the level of the DC bus voltage if one wants to control the rms
                      value of the output voltage v o .
                        There is however a way to control the rms value of the fundamental compon-
                      ent of the output voltage as well as the harmonic content of the fixed waveform
                      shown in Figure 6.27(a). In this method, the control signals of the two legs are not
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