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                                                            Power electronic control in electrical systems 211

                      Specifically, the converter consists of four switches (S a1 , S a2 , S a3 , S a4 ) and the
                      antiparallel diodes (D a1 , D a2 , D a3 , D a4 ). Due to the nature of the leg being able to
                      generate a three-level voltage waveform between the points A and O, two DC bus
                      voltage sources of equal value are required. This can be accomplished with two equal
                      value capacitors C 1 and C 2 where the initial DC bus voltage V dc is split across to
                      make two voltage sources of V dc /2 value available.
                        In previous sections, the phase-shifted control method (Figures 6.29 and 6.30) for a
                      single-phase full-bridge VSC shown in Figure 6.26 was explained. The interesting
                      point of such a technique is the ability to control the output voltage and its harmo-
                      nics contents by adjusting the angle a (degrees) where the line-to-line waveform
                      becomes zero.
                        It has been introduced in the technical literature that the number of levels of the
                      voltage between the mid-point of the converter leg and the DC bus mid-point (line-
                      to-neutral voltage waveform) is used to classify a given multilevel topology. The
                      conventional three-phase VSC as shown in Figure 6.32 is then a two-level converter
                      since it is capable of producing a two-level waveform between the two points men-
                      tioned above.
                        To clamp the voltage, two extra clamping diodes D ca1 and D ca2 as shown in Figure
                      6.34 are required to connect the DC bus mid-point to the load applying zero volts.
                      They also allow the current to flow in either direction when the converter operates in
                      the free-wheeling mode (zero volts at the output). For this case the load can be
                      connected between the points A and O like the case of the single-phase half-bridge
                      VSC shown in Figure 6.23.
                        The control for the three-level half-bridge VSC is slightly different and will be
                      explained next. It can be confirmed with the assistance of Figures 6.34 and 6.35 that





























                      Fig. 6.35 Key waveforms of the three-level single-phase half-bridge NPC VSC circuit operation. (a) output
                      voltage v o ˆ v AO ; (b) control signal for the switch S a1 ; (c) control signal for the switch S a2 ; (d) control signal for
                      switch S a3 ; and (e) control signal for switch S a4 .
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