Page 333 - Power Electronics Handbook

Output voltage control 323

Table 13.12 Harmonk content ofa sine modulated unidireetiorrpl wave rrithJTlfs = 20
~~ ~
R. M.S. voltage as percentage of d.c. supply

1 3 5 7 9 11 13 15 Total
0 0 0 0 0 0 0 0 0 0
0.1 7.58 0.68 1.04 0.22 0.33 0.26 0.38 1.26 25.9
0.2 14.9 0.60 0.09 0.50 0.35 0.30 0.62 0.48 36.2
0.3 21.5 0.15 0.15 o.n 0.53 0.52 0.88 0.24 43.7
0.4 28.2 0.03 0.56 0.89 0.00 0.01 1.02 0.55 50.2
0.5 35.3 0.05 0.00 0.41 0.53 0.15 0.47 0.50 56.2
0.6 42.4 0.16 0.05 0.21 0.22 0.13 0.82 0.53 61.6
0.7 49.2 0.10 0.22 0.39 0.29 0.15 0.85 0.97 66.3
0.8 56.8 0.53 0.59 0.26 0.06 0.36 0.28 0.09 71.2
0.9 64.0 0.55 0.02 0.15 0.49 0.21 0.13 0.76 75.5
0.98 69.0 0.26 0.42 0.19 0.10 0.16 0.32 1.25 78.6

Equations (13.13) and (13.15) are shown evaluated in Tables 13.9-13.12
for various values of the ratio f+’fs. Voltage control is again effected by
changing the ratio of AdAT. The maximum value of this ratio is limited to
0.98 rather than unity, to prevent adjacent pulses from merging into each
other.
Unlike all the previous systems, this method of voltage control results in
severe attenuation of frequencies below a certain value. The two-pulse
asymmetrical wave technique could be referred to as ‘selected harmonic
reduction’, since in this system the pulse spacing is so chosen as to
eliminate any required harmonic. The present system can be called ‘lower
harmonic reduction’, since it works to reduce harmonics below a certain
frequency. On examining the tables it will be seen that the harmonic
numbers with the largest amplitude occur at fiJfs k 1. Therefore, for
example, with f+’fs = 10 the harmonics are largest at the ninth and
eleventh. This is logical, since the tenth harmonic is the ‘camer’ wave
itself, and no attempt is made to eliminate it. Quite clearly, the higher the
ratio of f+’lfs, the more effective this system becomes. The same statement
was made when considering modulation with a square wave, but there the
effect of higher carrier frequencies was to keep the proportion of the
harmonics constant (and equal to the value for a square wave) as the
fundamental was varied, and not to eliminate it.
The system shown in Figure 13.40 has two disadvantages. First, the high
inverter frequency required to give effective lower harmonic reduction
leads to smaller efficiencies. Second, the maximum output voltage is well
below 90% of the d.c. supply, as obtained with a square wave. This would
limit the maximum operating frequency when running with some types of
loads which need to be fully fluxed. The system also shows a characteristic
increase in total harmonic content with higher operating frequencies. As
explained earlier, this is not normally serious since higher harmonics can be
more easily filtered out than lower-order ones.