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

3-L DC Link ML Converter Properties 57
example non perpendicular coordinate systems as proposed by N. Celanovic to simplify SVM
calculation [34]. A similar approach is also used in this thesis in chapter 5 for the SVM calculation.
Representation of space vectors in αβ is equivalent to a projection of the vector space onto a
plane. The projection of a cube onto a plane perpendicular to one of its large diagonals results in a
hexagon. Such a hexagon represents the physically possible operating range of most 3 phase
converters. Figure 48 and Figure 49 illustrate the above (maximum sinusoidal operation indicated
with a red circle). The trajectory of a sample vector sequence is shown, connecting the minimum
CM and maximum CM vectors {000} 3D to {444} 3D. The light green hexagon indicates the
intersection of the converter operation cube with the zero CM plane and indicates the limits of
operation with zero CM voltage (sinusoidal zero CM operation indicated by a blue circle).
b
β
0 1 2 3 4
4
3
2
1
0
0
α
1
2
c
4
3
Figure 48, Triangular vector sequence in αβ−frame
In the αβ-frame, the vector sequence (blue) is only visible as a triangle as only three different
DM voltage vector (equivalent to αβ-vectors) are applied. The CM voltage cannot be seen in that
representation. The DM output voltage and therefore a 2-D representation of the converter state is
sufficient for the control of the load (current, torque, etc.).
0
b
1
2
β
3
0
4
4
3
2
4
1
3
2
0
0
1
α
a
4
3
2
b
1
0
4
3
2
β
c
0 0
2
3
4
a
α
4
3
2
1
b
0
4
3
2
c
2
3
a
4
1
1
1
1
c
0 0
(a) (b) (c)
0
0
Figure 49, Cube in abc-frame with spiral vector sequence