Operation and Design of Multilevel Inverters Dr ... - MotorLab.com

⎡v
⎢
⎢
v
⎢⎣
v
ab
bc
ca
⎤ ⎡ 1
⎥ ⎢
⎥
=
⎢
0
⎥⎦
⎢⎣
−1
−1
0 ⎤⎡v
⎢
−1
⎥
⎥⎢v
1 ⎥⎢
⎦⎣
v
Copyright 2005. K.A. Corzine 4
1
0
ag
bg
cg
⎤
⎥
⎥
⎥
⎦
(3.1-3)
Figure 3.1-3 shows the switching state, line-to-ground voltage, line-to-neutral
voltage, and line-to-line voltage for the case where n = 9 . Therein, the line-toground
voltage contains a third harmonic component which is added in order to
maximize the inverter output voltage [27]. Therein, it can be seen that the line-toneutral
and line-to-line voltages do not contain the third harmonic. Also, it is
interesting to note that these voltages contain more levels than the original line-toground
voltages. It is easily understood that there are 2n −1
line-to-line voltage
levels consisting of n positive levels, n negative levels, and zero. In Figure 3.1-3,
these seventeen voltage levels can be clearly seen in v ab . As it turns out, there are
4n − 3 line-to-neutral voltage levels which works out to thirty-three for the ninelevel
inverter. However, the switching between the levels is not perfectly even since
all three phases are involved.