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

94 NP Control with Carrier based PWM
Song [76] analytically calculates the suitable zero sequence to be injected. The NP current is
calculated as in (55), but rather than identifying the most interesting part of the piecewise linear
function. Song uses a test-verify-revise algorithm where he starts from an initial assumption for the
result of the sign functions in (55) and then revises if necessary. The actual NP control algorithms
tries to generate a NP current to get to zero NP voltage deviation within one modulation period. If
the controller goes into saturation, the CM voltage is only limited to the physical limitation, which
will result in very poor performance of the scheme proposed in reactive power operation.
5.2 Harmonic injection NP control
The previous paragraph has described a new CM injection scheme based on the real time NP
current function with all calculations done in time domain, . As an alternative, an approach in the
frequency domain is proposed in this paragraph.
In active power operation, the gradient in the NP current function remains the same
throughout the whole period, a DC CM offset creates a DC NP current and a linear feedback
control can be used directly. In reactive power operation, a DC CM offset creates an AC NP
current. To generate a DC NP current, higher order harmonics need to be injected instead. This is
true also for the real-time NP current scheme presented in the previous paragraph, where the CM
function is generated purely in the time domain. Also in that case, a set of higher order harmonics
are injected as a result of the NP control. However, they do not need to be known at the time of
application.
As an alternative, specific harmonics could be injected. A fundamental component needs to be
generated in the rectified switching function to interact with the fundamental output current and
generate a DC NP current (see TABLE 27). In active power operation, such a fundamental can easily
be generated with a DC offset (see TABLE 24). For reactive power operation, a DC offset is not
effective, as the fundamentals in the rectified switching function and the fundamental output
current will have a phase shift of π/2. A fundamental without phase shift needs to be generated.
TABLE 31 gives three example of harmonic injection for the generation of a suitable
fundamental component in the rectified function. The first example on the left used calculated
harmonics from 2 nd to 15 th order based on a pure DC and fundamental in the rectified switching
function. Obviously, the result is very powerful regarding NP control but the associated highly
distorted switching function is not applicable in reality as it would generate a very large distortion in
output voltage and current. In practice only zero sequence components are allowed and only with
an amplitude that can physically be generated. The second column of TABLE 31 does exactly that by
applying optimized multiples of 3 rd harmonics up to the 42 nd . The result is close to the ideal case
which would be obtained by application of the real time NP current scheme with high gain. The
CM jumps mentioned in paragraph 5.1.2 are actually nicely visible also with this harmonic injection
approach (as relatively high frequencies are injected). The third column in TABLE 31 injects only a
3 rd and a 6 th harmonic. The resulting waveforms resemble the ones obtained with the harmonic
injection up to the 42 nd , but obviously it is much smoother and likely to generate less switching
losses.
It is interesting to note that both cases result in almost the same value for the fundamental
component in the rectified switching function. This indicates that the 6 th harmonic is dominant
over the higher order harmonics regarding the generation of a fundamental component.