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

3-L DC Link ML Converter Properties 75
The individual gradients per phase are:
s
dI
( s )
I
2I
NPx x outx outx
x
< 0 → = =
(65)
dsCM
U
DC
2 U
DC
s
x
dI
( s )
I
2I
NPx x
outx
outx
> 0 → = − = −
(66)
dsCM
U
DC
2 U
DC
Using (63), (64), (65), and (66) we get:
s
s
dI
I
NP _ tot
4
out _ x
x
< 0 ∧ s
y
> 0 ∧ sz
> 0 → =
(67)
dsCM
U
DC
dI
I
NP _ tot
4
out _ z
x
< 0 ∧ s
y
< 0 ∧ sz
> 0 → = −
(68)
dsCM
U
DC
The gradient in the NP current function is always defined by the current in the phase with the
unique sign in the average switching function. The two gradients in the middle section may have
the same sign or a different sign, which means the function may be monotonic or non monotonic,
depending on operating point. An analysis of all possible operating points shows that nonmonotonic
behavior occurs for low cos(ϕ). This function can be determined for every operating
point with any given voltage and current vector. The function is dynamically changing with time.
Accordingly, any control scheme making use of the true NP current function must either determine
it online or pre-calculate all possible operating points. One example is given in Figure 62. An
overview of different operating points is given in appendix 9.6.
Figure 62, NP current as function of θ and CM voltage, m = 0.3, ϕ = 1.4
4.7.2 NP current characteristics as a function of m, ϕ and θ
Maximum and minimum achievable NP currents are a measure for the controllability of the
NP voltage. High NP currents enable a fast change (and thus control) of the NP voltage. Minimum