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

ML Converter Topologies 39
3.7.4.1 Flying capacitor energy for MC based converters
All capacitors within one MC structure are operated with the same duty cycle and all capacitors
may have the same absolute voltage ripple (independently of their voltage rating), which means the
relative ripple decreases with increasing voltage. This is required to avoid over voltages on the
switches of the individual cells. Consequently, all capacitors require the same capacitance C 0. In the
case of the MC converter with interleaved operation, the following basic equations apply to all
flying capacitors:
I
FC
∆U
= C *
FC
0 (8)
∆tFC
U
∆t
DC
FC _ max
∆ U
FC _ max
= k1
= I
FC _ max
(9)
N
C
0
With k 1 indicating the allowable maximum ripple ratio in function of the supply voltage and
1/N.
tFC _ max
= k2T SP
∆ (10)
With T SP as switching period time and k 2 indicating the maximum capacitor application time
ratio in function of the switching period.
C
∆t
I Nk T I
FC _ max
Nk2
= (11)
k U f
FC _ max FC _ max 2 SP
0
I
FC _ max
=
=
∆U
FC _ max
k1U
DC
1
DC
sw
All parameters determining C 0 are either given from the system (I, N, U DC) or can be chosen as
operation parameter (k 1, f sw); k 2 depends on the topology. It indicates the largest expected
application time ratio of the capacitor before current reversal in the capacitor is possible. The
following graph illustrates the maximum capacitor application time ratio in an MC converter.
Flying capacitors are charged or discharged by the corresponding output current, whenever the
two adjacent cells do not have the same state. The current bypasses the flying capacitor when the
two adjacent cells have the same state (either low or high). Figure 36 shows the example of a 4 cell
MC converters with 4 carriers with regular phase shifts (π/2 between adjacent cells) and 5 sample
references. For a given reference, the maximum capacitor application time corresponds with the
phase shift between adjacent carriers, which is indicated with the bold sections of the reference
lines. It can be seen from the figure that the capacitor application time is constant in the
intermediate part of reference and going linearly to zero towards the upper and lower limits. The
sign of the current in the flying capacitor can be chosen every time a state using a flying capacitor is
applied.