modele matematyczne energoelektronicznych przekształtników ...

Modele matematyczne energoelektronicznych przekształtników wielopoziomowych. Analiza ... 141
The analytical model of the two-level three-phase converter for discrete
waveforms, based on a set of expressions describing in time domain voltage
and current waveforms in the converter-load circuitry. The model is useful
in analysis of stationary and transitory states of digitally controlled voltage
and current source converters and also for research in the field of real-time
control algorithms. The idea of this model has been used for elaborating the
models of multilevel converters.
The model of three-level converter with the discussion concerning
output voltage waveforms formed by use the transformation of polar
voltages to complex stationary coordinates system (α , β ). The expressions
describing the three-level and five-level converter models in time domain
have been formulated. The further development of the presented ideas
enabled the construction of universal n-level converter model. The proposed
unified denoting system for output voltage space vectors of multilevel
converters makes possible the fast analysis of space vectors positions on
complex plane and finding the number of multiplied vectors.
The Fourier-style model is based on the approximation of the function
f (x) = sin(x) using series of the square-wave pulses described by series of
g n (x) functions. The parameters of this series have been calculated with
Fourier factors of the orthogonal series composed from the g n (x) functions.
The harmonic spectra of the converter’s output voltages have been analyzed.
As a result of this analysis the proposal of a new THD factor has been
presented. The new THD factor facilitates the estimation of the step
waveforms from the filtration point of view. The examples of the converter
structures using Fourier-style model for synthesis of alternating voltage
waveforms have been presented.
The wavelet-style model is using the new mathematical tool – a wavelet
transform for the step waveforms synthesis. The defined wavelet-style model
of the converter is based on transform similar to the Haar transform. By
properties comparison of Fourier-style and wavelet-style models it was
proved, that approximation method, based on wavelet theory is a useful
mathematical tool in developing the structures and control algorithms of the
multilevel converters.
The orthogonal model is based on adding the orthogonal vectors and
further development of this idea resulted in the recurrent model. The
structures and control methods of these converters are promising
alternatives for other well known multilevel converters’ solutions.
The defined mathematical models are describing the output voltages of
multilevel converters as results of the combination of the orthogonal
functions (Fourier-style and wavelet-style models) or orthogonal vectors
(recurrent model). Thanks to this approach the presented models show
cleanly the relations between the component voltage waveforms and output
voltage waveform of the whole converter. It facilitates designing the
structures and control algorithms and allows to treat the multilevel
converter as one unit.
The examples of circuitry solutions based on defined models as well as
simulation and experimental results of the chosen converters are also
presented in the monograph.