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

3-L DC Link ML Converter Properties 73
The individual NP current function can be represented in a single graph with normalization
with one of the three phase currents (e.g. the largest one) as indicated in Figure 60. The average
switching function s is going from -1 to 1 for each phase.
I NP
1
I-NP1 / I-out1
0
-1
0
s
1
I-NP2 / I-out1
I-NP3 / I-out1
-1
Figure 60, NP point currents in 3 phase system
It can be seen from (57) and Figure 60 that not only the output currents add up to zero, but
also the gradients of the piecewise linear functions, if all s have the same sign.
x
di
di
( s1
< 0) diNP
2(
s2
< 0) diNP3(
s3
+
+
ds
ds
ds
< 0)
NP 1 =
CM
CM
CM
( s1
> 0) diNP2(
s2
> 0) diNP3(
s3
+
+
ds
ds
ds
> 0)
NP 1 =
CM
CM
CM
0
0
(58)
(59)
The gradient functions for each phase only take on two distinct values, one positive and one
negative number of the same absolute value with positive and negative sign. If a differential output
voltage is given, the NP current can be calculated in function of the CM voltage. This means a CM
term s can be added to the given set of average switching functions. Based on the above, we can
CM
state that the gradient of the overall NP current function is constant for varying s as long as
CM
none of the resulting phase modulation indices crosses the zero point. Each zero crossing the
average switching function in any of the phases changes the overall NP current gradient, unless the
current in the corresponding phase is zero. The resulting function is a piecewise linear function
with a maximum of 3 singularities and 4 linear sections. The actual physically available range of that
function is constrained as none of the voltages may assume values outside of the DC link voltage
range. Therefore, five operating points define the Neutral point current in function of the applied
common mode voltage (see Figure 61, five points per phase, P1 to P5). These points are defined by
any one phase assuming the value -1, 0 or 1. This is valid independently of the balance and
symmetry of the system, as it uses instantaneous values. Each color in Figure 61 is representing a
certain common mode voltage (the line indicating the common mode voltage, the dots representing
the individual average switching functions and the NP currents of the three phases).