Conventional three-phase six-step VSC

The conventional three-phase six-switch VSC is shown in Figure 6.32. It consists of six switches S₁-S₆ and six antiparallel diodes D₁-D₆. The number indicates their order of being turned on. A fictitious neutral (o) as a mid-point is also included although in most cases is not available. However, when the converter under consideration is used as an active filter in the case of a four-wire three-phase system, this point (o) is used to connect the fourth-wire. This case will be discussed further in later parts.

The three converter legs are controlled with a phase-shift of 120^o between them. The basic way to control the three-phase six-switch VSC is to turn on each switch for half of the period (180⁰) with a sequence 1, 2, 3, . . . as they are numbered and shown in Figure 6.32.

Fig. 6.32  Conventional three-phase six-switch VSC.

The operation of the converter can be explained with the assistance of Figure 6.33. Specifically, the control signals for each of the six switches are shown in Figure 6.33(a). Clearly, each switch remains on for 180⁰ and every 60⁰ a new switch is turned on and one of the previous group is turned off. At any given time therefore, one switch of each leg is on. Assuming that the fictitious mid-point (0) is available, three square-type waveforms for the voltages v_AO, v_BO, and v_CO can be drawn as shown in Figure 6.33(b). Each of the voltage waveforms has two peak values of V_dc/2, and -V_dc/2, and they are displaced by 120^o from each other.

From the three waveforms v_AO, v_BO, and v_CO, the line-to-line voltage waveforms can be drawn since

The three resultant line-to-line voltage waveforms are then shown in Figure 6.33(c). It is clear that each waveform takes three values (V_dc, 0, -V_dc) and there is a 120^o phase-shift between them. These waveforms have a 60^o interval when they are zero for each half of the period, a total of 120o per period. As explained earlier, each leg can handle current in both directions at any time, since either the turned on switch or the antiparallel diode of the other switch can be the conducting element depending upon the polarity of the output line current.

The potential of the load neutral point (n) shown in Figure 6.32 with respect to the mid-point of the DC bus (0) is drawn in Figure 6.33(d). It can be seen that such a waveform has frequency three times the output frequency and the two peak values are between V_dc/6 and -V_dc/6. Finally, the line-to-load neutral point (n) voltage waveform is illustrated in Figure 6.33(e). Such a voltage waveform has two positive values (V_dc/3 and 2V_dc/3) and two negative ones (-V_dc/3 and -2V_dc/3).

Fig. 6.33 Key waveforms of the three-phase six-step VSC circuit operation. (a) control signals for switches S₁, S₂, S₃, S₄ ,S₅ , S6; (b) voltage waveforms v_AO, v_BO, and v_CO; (c) output line-to-line voltage waveforms v_AB, v_BC, v_CA ; (d) voltage waveform between the load neutral point (n) and the DC bus mid-point (0); (e) voltage waveform between the line point A and the load neutral point n; (f) harmonic spectrum of the line-to-DC bus mid-point; and (g) harmonic spectrum of the line-to-line voltage v_AB.

The harmonics of the various waveforms can be calculated using Fourier series. The fundamental amplitude of the voltage waveforms v_AO, v_BO, and v_CO is

where h is the order of the harmonic.
For the line-to-line voltage waveforms v_AB, v_BC, and vCA  then the fundamental amplitude is

and therefore the rms value of the fundamental component is then

Similarly, the amplitude of the harmonic voltages is

The rms value of the line-to-line voltage including all harmonics is

The  normalized  spectrum  of  the  line-to-DC  bus  mid-point  and  the  line-to-line voltage waveforms are plotted in Figures 6.33(f) and (g) respectively. It can be seen that the voltage waveforms v_AO, v_BO, and v_CO contain all odd harmonics. The load connection as shown in Figure 6.32 does not allow 3rd harmonic and all multiples to flow, and this is confirmed with the spectrum of the line-to-line voltage waveform v_AB where 3rd, 9th and 15th harmonics are eliminated as shown in Figure 6.33(g).
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