Christoph Haederli - Les thèses en ligne de l'INP - Institut National ...

3-L DC Link ML Converter Properties 81
- A DC component in the input current
- Higher order harmonics in input current and rectified switching function can be used
- A fundamental with a π/2 (plus/minus) phase shift can be generated in the rectified
switching function
The first possibility is not practical, as most applications do not allow having a DC CM
current. The other two concepts are addressed in the following paragraphs.
4.8.2 Harmonic injection analysis
With a dominant fundamental component all harmonics are multiplied with the sign of the
fundamental when rectified. This is illustrated with the example of a 6 th harmonic component in
TABLE 25.
TABLE 25, HARMONICS IN RECTIFIED SWITCHING FUNCTION ABS(S(T)) IN FUNCTION OF
HARMONIC CONTENT OF S(T)
Combined function Fundamental component Harmonic component
Switching
function
1
0.5
Switching function
1
0.5
Switching function
1
0.5
Harmonic injection
(t) s x
sx
0
sx
0
pu
0
-0.5
-0.5
-0.5
-1
-1
-1
0 1 2 3 4 5 6
Time
(a)
0 1 2 3 4 5 6
Time
(b)
0 1 2 3 4 5 6
Time
(c)
Rectified
switching
function
abs( s x
( t))
abs(sx)
1
0.8
0.6
0.4
0.2
0
Rectified switching function
abs(sx)
1
0.8
0.6
0.4
0.2
0
Rectified switching function
abs(sx)
1
0.8
0.6
0.4
0.2
0
Transformed harmonic function
-0.2
0 1 2 3 4 5 6
Time
(d)
-0.2
0 1 2 3 4 5 6
Time
(e)
-0.2
0 1 2 3 4 5 6
Time
(f)
Spectrum of
rectified
switching
function
pu
Amplitude spectrum of rectified switching function
0.7
0.6
0.5
0.4
0.3
0.2
pu
Amplitude spectrum of rectified switching function
0.7
0.6
0.5
0.4
0.3
0.2
pu
Amplitude spectrum of rectified switching function
0.6
0.5
0.4
0.3
0.2
0.1
S 0
x(ω)
0 5 10 15 20
Harmonic order
(g)
0.1
0
0 5 10 15 20
Harmonic order
(h)
0.1
0
0 5 10 15 20
Harmonic order
(i)
The total (complex) harmonic spectrum of the rectified switching function S rect_x(ω) is the sum
of spectra of the individual transformed fundamental and harmonic components S trans_x_n(ω), n
indicating the harmonic order number starting from 1 (the DC component is zero as previously
defined). Each phase has its own spectrum with x being the index for one of the three phases.
with
S
= ∑ ∞ ( ω ) Strans
_ x _ n(
ω
(73)
n=1
rect _ x
)