Page 322 - Power Electronics Handbook

312 D.C. link frequency changers

Tsbk 13.1 Hamonk eompositiop of s quad-qusre rsve
2DIT R. M.S. voltage percentage of d.c. supply

1 3 5 7 9 11 13 15 Total
0.00 90.0 30.0 18.0 12.9 10.0 8.18 6.92 6.00 100
0.02 89.8 29.5 17.1 11.6 8.44 6.30 4.74 3.53 98.0
0.04 89.3 27.9 14.6 8.20 4.26 1.53 0.43 1.85 95.9
0.06 88.4 25.3 10.6 3.20 1.25 3.94 5.33 5.71 93.8
0.08 87.2 21.9 5.56 2.41 6.37 7.61 6.87 4.85 91.7
0.10 85.6 17.6 0.00 7.56 9.51 7.78 4.07 0.00 89.4
0.12 83.7 12.8 5.56 11.3 9.69 4.38 1.30 4.85 87.2
0.14 81.4 7.46 10.6 12.8 6.85 1.03 5.85 5.71 84.9
0.16 78.9 1.88 14.6 12.0 1.87 5.96 6.71 1.85 82.5
0.18 76.0 3.76 17.1 8.80 3.68 8.17 3.34 3.53 80.0
0.20 72.8 9.27 18.0 3.97 8.09 6.62 2.14 6.00 77.5
0.22 69.3 14.5 17.1 1.61 9.98 2.03 6.26 3.53 74.8
0.24 65.6 19.1 14.6 6.89 8.76 3.48 6.44 1.85 72.1
0.26 61.6 23.1 10.6 10.9 4.82 7.40 2.55 5.71 69.3
0.28 57.4 26.3 5.56 12.8 0.63 7.92 2.95 4.85 66.3
0.30 52.9 28.5 0.00 12.2 5.88 4.81 6.58 0.00 63.2
0.32 48.2 29.8 5.56 9.37 9.30 0.51 6.07 4.85 60.0
0.34 43.4 29.9 10.6 4.73 9.82 5.60 1.72 5.71 56.6
0.36 38.3 29.1 14.6 0.81 7.29 8.12 3.71 1.85 52.9
0.38 33.1 27.1 17.1 6.19 2.49 6.91 6.80 3.53 49.0
0.40 27.8 24.3 18.0 10.4 3.09 2.53 5.60 6.00 44.7
0.42 22.4 20.5 17.1 12.6 7.71 3.01 0.87 3.53 40.0
0.44 16.9 16.1 14.6 12.5 9.92 7.17 4.41 1.85 34.5
0.46 11.3 11.0 10.6 9.91 9.05 8.04 6.91 5.71 28.3
0.48 5.65 5.62 5.56 5.47 5.36 5.22 5.05 4.85 20.0
0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Equations (13.5) and (13.6) are shown evaluated in Table 13.1 up to the
15th harmonic, where the period T equals a. From this table it is evident
that the harmonic content of the output increases rapidly as the
mark-to-space ratio of the waveform is reduced. This is illustrated more
clearly in Figure 13.34, which shows the plot of the harmonics, obtained
from Table 13.1. Because in reality it is the magnitude of the fundamental
which is of interest rather than the mark-to-space ratio, which is a means of
varying the fundamental, it is more normal to show harmonic plots against
the fundamental, and this is done for the harmonics of Table 13.1 in Figure
13.35.
At low voltages various harmonics are almost equal in value to the
fundamental, the total harmonic content being about ten times larger. This
represents the greatest disadvantage of the quasi-square voltage-control
system, and normally limits the output voltage range to between 30% and
90% of the d.c. supply, Le. a frequency change of 3:l in applications where
the voltage needs to be varied proportional to the frequency of the load.
Figure 13.33 is also referred to as a single-pulse unidirectional wave. It is
unidirectional since in any half cycle the output is either positive or
negative, but never both, and there is a single pulse in each half cycle. An
obvious extension to this system is shown in Figure 13.36, which illustrates