Christoph Haederli - Les thèses en ligne de l'INP - Institut National ...
Christoph Haederli - Les thèses en ligne de l'INP - Institut National ...
Christoph Haederli - Les thèses en ligne de l'INP - Institut National ...
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42 ML Converter Topologies<br />
In a fully redundant MC converter, the voltage sequ<strong>en</strong>ce in the capacitors is giv<strong>en</strong>:<br />
yU<br />
U = DC<br />
y<br />
N<br />
(21)<br />
This can be inserted in the equation above<br />
2<br />
k / p<br />
k / p<br />
pN ⎛ yU ⎞<br />
DC<br />
p<br />
2<br />
K = ∑<br />
⎜<br />
⎟<br />
E cap<br />
= ∑ y<br />
(22)<br />
_<br />
Mk<br />
f _ sw y=<br />
1 ⎝ NU<br />
DC ⎠ MNk<br />
f _ sw y=<br />
1<br />
3<br />
( k / p) ( k / p)<br />
2<br />
p ⎛<br />
⎞<br />
⎜<br />
k / p<br />
K =<br />
⎟<br />
E _ cap<br />
+ +<br />
(23)<br />
MNk<br />
f _ sw ⎝ 3 2 6 ⎠<br />
E<br />
tot<br />
I<br />
U<br />
⎛<br />
3<br />
( k / p) ( k / p)<br />
2<br />
FC _ max DC p<br />
k / p FC _ max DC<br />
= KE<br />
_ cap<br />
= ⎜<br />
k fsw<br />
base<br />
MNk<br />
+ +<br />
(24)<br />
1 _<br />
f _ sw<br />
3 2 6 2k1<br />
fsw<br />
_ base<br />
2 ⎟ ⎝<br />
⎠<br />
⎞ I<br />
U<br />
Thanks to the parameterization, these equations can be used to calculate the total flying<br />
capacitor <strong>en</strong>ergy for a wi<strong>de</strong> range of differ<strong>en</strong>t topologies. The meaning of parameters shall be<br />
repeated here for clarity:<br />
TABLE 19, PARAMETER DEFINITIONS<br />
p<br />
k<br />
M<br />
N<br />
k f_sw<br />
number of id<strong>en</strong>tical groups of MC converters (non overlapping)<br />
total number of flying capacitors<br />
number of cells that can be operated interleaved<br />
input voltage divi<strong>de</strong>d by smallest capacitor voltage (number of cells in pure MC converter)<br />
switching frequ<strong>en</strong>cy factor to get actual maximum switching frequ<strong>en</strong>cy from maximum<br />
switching frequ<strong>en</strong>cy that can be used in the MC converter (f sw_base)<br />
k 1<br />
maximum allowable voltage ripple ratio ∆U/U N<br />
Dep<strong>en</strong>ding on the giv<strong>en</strong> boundary conditions differ<strong>en</strong>t parameters may be used. The following<br />
paragraphs list the resulting capacitor <strong>en</strong>ergies for three differ<strong>en</strong>t operating conditions: Operational<br />
limitation by peak switching frequ<strong>en</strong>cy of <strong>de</strong>vice, operational limitation by average switching<br />
frequ<strong>en</strong>cy of <strong>de</strong>vice and operational limitation by appar<strong>en</strong>t output switching frequ<strong>en</strong>cy of<br />
converter. The corresponding tables are giv<strong>en</strong> in app<strong>en</strong>dix 9.2.1.<br />
3.7.4.1.1 Operational limitation by peak <strong>de</strong>vice switching frequ<strong>en</strong>cy<br />
Operational limitation of a converter may be giv<strong>en</strong> by the peak <strong>de</strong>vice switching frequ<strong>en</strong>cy.<br />
This limitation may be based on two differ<strong>en</strong>t reasons. The first one being gate driving limitation,<br />
for example in the case where IGCT are used. IGCT gate drivers always have limited operating<br />
frequ<strong>en</strong>cy, optimized according to a tra<strong>de</strong> of betwe<strong>en</strong> cost and performance in its target application.