Page 272 - Rashid, Power Electronics Handbook

14 Inverters 261

FIGURE 14.53 Three-phase-input single-phase output cell: (a) power topology; (b) ac input current, phase a; (c) ac output voltage (m f ¼ 6,
m a ¼ 0:8).

Figure 14.54 shows a multicell converter that generates a harmonics 6 m in the load-phase voltage v , that is, the
an
f
three-phase output voltage out of a three-phase ac distribution lowest set of harmonics in Fig. 14.55f) is 6 m ¼ 6 6 ¼ 36.
f
system. The structure uses three standard cells (as shown in This can be explained as follows. The voltage harmonics
Fig. 14.53) connected in series to form one phase; thus the present in the PWM voltage of each cell are at l m k,
f
phase-load voltages are the sum of the single-phase voltages l ¼ 2; 4; ... (where k ¼ 1; 3; 5; ...); for instance, for m ¼ 6,
f
generated by each cell. For instance, the phase voltage a is the ®rst set of harmonics is at 12 1; 12 3; ... in all cells.
given by Because the cells in one phase use carrier signals that are 120
out of phase, all the voltage harmonics l m in all cells are
f

v an ¼ v o11 þ v o21 þ v o31 ð14:87Þ l 120 out of phase. Therefore, for l ¼ 2, the cell c 11 generates
the harmonics l m k ¼ 2 m k at a given phase j, the
f f
In order to maximize the load-phase voltages, the ac cell c generates the harmonics 2 m k at a phase
21 f

voltages generated by the cells should feature identical funda- j þ l 120 ¼ j þ 2 120 ¼ j þ 240 ¼ j ÿ 120 , and the
mental components. On the other hand, each cell generates a cell c generates the harmonics 2 m k at a phase
21 f

PWM voltage waveform at the ac side, which contains j ÿ l 120 ¼ j ÿ 2 120 ¼ j ÿ 240 ¼ j þ 120 ; thus, if
unwanted voltage harmonics. If a carrier-based modulating the voltages have identical amplitudes, the harmonics
technique is used, the harmonics generated by each cell are at 2 m add up to zero. Similarly, for l ¼ 4, the cell c 11
f
well-de®ned frequencies (Fig. 14.53c). Some of these harmo- generates the harmonics l m k ¼ 4 m k at a given
f
f
nics are not present in the phase-load voltage if the carrier phase j, the cell c 21 generates the harmonics 4 m k at a
f

signals of each cell are properly phase shifted. phase j þ l 120 ¼ j þ 4 120 ¼ j þ 480 ¼ j þ 120 ,
In fact, Fig. 14.55 shows the voltages generated by cells c , and the cell c 21 generates the harmonics 4 m k at a
11
f

c , and c , which are v o11 o21 , and v o31 , respectively, and form phase j ÿ l 120 ¼ j ÿ 4 120 ¼ j ÿ 480 ¼ j ÿ 120 ;
,
21
31
the load-phase voltage a. They are generated using the unipo- thus, if the voltages have identical amplitudes, the harmonics
lar SPWM approach, that is, one modulating signal v ca and 4 m add up to zero. However, for l ¼ 6, the cell c 11
f
three carrier signals v , v , and v D3 that are used by cells c , generates the harmonics l m k ¼ 6 m k at a given
D1
D2
f
11
f
c , and c , respectively (Fig. 14.55a). The carrier signals have phase j, the cell c 21 generates the harmonics 6 m k at a
f
21
31

a normalized frequency m , which ensures an m switching phase j þ l 120 ¼ j þ 6 120 ¼ j þ 720 ¼ j, and the
f
f
frequency in each power valve and the lowest unwanted set of cell c 21 generates the harmonics 6 m k at a phase
f

harmonics 2 m ðm evenÞ in the ac cell voltages v o11 , v o21 , j ÿ l 120 ¼ j ÿ 6 120 ¼ j ÿ 720 ; thus, if the voltages
f
f
and v o31 . More importantly, the carrier signals are c ¼ 120 have identical amplitudes, the harmonics 6 m become
f
out of phase, which ensures the lowest unwanted set of voltage triplicated rather than cancelled out.