Signal Injection

2 Signal Injection

The restriction for m a (m a ≤ 1) can be relaxed if a zero The ac line output voltage contains the harmonics f h , where sequence signal is added to the modulating signals before

h = 6 · k ± 1 (k = 1, 2, 3, . . .) and they feature amplitudes they are compared to the carrier signal. Figure 15.16 shows that are inversely proportional to their harmonic order the block diagram of the technique. Clearly, the addition of

370 J. R. Espinoza S 1

1.1v i

(d) FIGURE 15.15 The three-phase VSI. Square-wave operation: (a) switch S 1 state; (b) switch S 3 state; (c) ac output voltage; and (d) ac output voltage

v 0 max{ }/3

0.88 ωt 0.17 ωt

FIGURE 15.16 Zero sequence signal generator (m a = 1.0, m f = 9): (a) block diagram; (b) modulating signals; and (c) zero sequence and modulating signals with zero sequence injection.

the zero sequence reduces the peak amplitude of the result- amplitude of the fundamental ac output line voltage is v i .

ing modulating signals (u ca ,u cb ,u cc ), while the fundamental Therefore, one can write

components remain unchanged. This approach expands the range of the linear region as it allows the use of mod-

ˆv ab1 =m a 3 0<m a ≤ 2/ 3 (15.34) ulation indexes m a up to 2/

3 without getting into the

overmodulating region. The maximum amplitude of the fundamental phase voltage √

Figure 15.17 shows the ideal waveforms of a three-phase VSI in the linear region

a ≤ 2/ 3 i /2, thus, the maximum SPWM with zero injection for m a = 0.8.

0.8·0.866·v i

FIGURE 15.17 The three-phase VSI. Ideal waveforms for the SPWM (m a = 0.8, m f = 9) with zero sequence signal injection: (a) modulating signals; (b) carrier and modulating signals with zero sequence signal injection; (c) switch S 1 state; (d) ac output voltage; (e) ac output voltage spectrum; (f) ac

output current; (g) dc current; (h) dc current spectrum; (i) switch S 1 current; and (j) diode D 1 current.

15.3.4 Selective Harmonic Elimination in Three-phase VSIs

could be present in the phase voltages (v aN ,v bN , and v cN ), will not be present in the load voltages (v ab ,v bc , and v ca ). Therefore, As in single-phase VSIs, the SHE technique can be applied these harmonics are not required to be eliminated, thus the to three-phase VSIs. In this case, the power valves of each chopping angles are used to eliminate only the harmonics at leg of the inverter are switched so as to eliminate a given frequencies h = 5, 7, 11, 13, . . . as required. number of harmonics and to control the fundamental phase-

The expressions to eliminate a given number of harmon- voltage amplitude. Considering that in many applications, the ics are the same as those used in single-phase inverters. For required line output voltages should be balanced and 120 ◦ out instance, to eliminate the fifth and seventh harmonics and per- of phase, the harmonics multiples of 3 (h = 3, 9, 15, . . .), which form fundamental magnitude control (N = 3), the equations

372 J. R. Espinoza v aN

0.8·v i

FIGURE 15.18 The three-phase VSI. Ideal waveforms for the SHE technique: (a) phase voltage v aN for fifth and seventh harmonic elimination;

(b) spectrum of (a); (c) line voltage v ab for fifth and seventh harmonic elimination; and (d) spectrum of (c).

to be solved are:

15.3.5 Space-vector (SV)-based Modulating