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On the other hand, if the fundamental modulation index is less than 0.6459, it can be
completely cancelled out by inserting the same amplitude of the 3rd harmonic component. For
example, M 0 =0.6459, maximum M 3 can also be 0.6459.
Figure 8.7 shows the simulation results when traditional pulsewidth modulation method is
used, and the fundamental modulation index is 0.9, which is at the higher end. The top 3
waveforms show the line-to-line voltage, measured to be at 12.7 kV. The 2nd 3 waveforms are
the capacitor currents in the top modules of each phase. Numerical simulation shows the rms
value of this ripple current that the dc link capacitor has to absorb is 47.2 A. The 3rd 3
waveforms demonstrate the phase voltage of the multilevel inverter, and the rms value is
measured to be 7.3 kV. And the 4th 3 waveforms show the 3 phase inverter output current. The
last waveform shows the dc link voltage for the top module in Phase A, which indicates the
voltage ripple peak-to-peak versus the dc link average voltage is around 2%.
Vripple( pp )
Vdc( avg )
=
34.329 V
= 2.0%
1648.2 V
(8.16)
This percentage is consistent for other modules as well.
From this simulation result, it is concluded that to maintain the dc link voltage ripple under
2% at this situation, the dc link capacitor for each H-bridge module has to be at least 3.8 mF.
Accordingly, in per unit value, this capacitance is
3.8 mF
= 18.5 p.u.
205 µ F
124
(8.17)
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