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

98 NP Control with Carrier based PWM
For low modulation depth and cos(ϕ) not equal to zero, both outer sections of the piecewise
linear function have the same absolute value but opposite signs. Maximum and minimum current
functions (with lowest absolute value CM) are clearly defined. These maximum and minimum
current functions have singularities with CM jumps as can be seen from TABLE 34. Nevertheless,
continuous CM voltage operation is possible with suitable 3 rd harmonic injection, as proposed in
TABLE 34. The third harmonic required has significantly different amplitude and phase angle than
the one use in TABLE 32. Of course, other strategies of CM injection staying within the minimum
and maximum boundaries are possible, but a strategy leading to continuous CM injection function
is preferable for commutation reasons; any jump in the CM function will generate multiple
commutations simultaneously and lead to higher overall switching losses.
Note that minimum and maximum NP current CM values do not cross each other in this case
(as opposed to the approach in TABLE 32). Consequently, no AC CM needs to be injected to
generate a DC NP current, but a pure DC CM voltage injection can be used both for minimum and
maximum DC NP current. This is shown in the third column TABLE 34. Note that there is a
smooth transition possible from active to reactive power with this control scheme. The 3 rd
harmonic amplitude and phase can be defined as a continuous function of amplitude of the
fundamental and the angle ϕ between voltage and current.
The 6 th harmonic injection scheme can still be applied at low modulation depth and non zero
cos(ϕ) if the CM function for minimum and maximum NP current are adapted accordingly,
conforming with the constraints above. In fact the examples in TABLE 32 use a phase angle of 1.56,
which leads to small but noticeable difference of NP currents in the two outer sections of the NP
current functions. The performance impact is very low. Both schemes have very similar
performance. The 6 th harmonic injection scheme will have slightly reduced maximum and minimum
NP currents but it has a higher degree of freedom regarding 3 rd harmonic injection and it requires
no DC CM injection for the NP control.
We can conclude that there are two almost equivalent concepts for NP current control for
reactive power operation at low modulation depth. This is not true for high modulation depth,
because the outer sections of the piecewise linear CM current function cannot physically be
reached. Consequently, the minimum and maximum NP current functions are clearly defined. Only
6 th harmonic injection is possible as shown in TABLE 33.