Modern industrial applications of dc-ac inverters have increasing demands for high quality output voltages and currents. Such demands are met through operating inverters so that output harmonic components are either reduced or eliminated. Developing and testing switching strategies capable of achieving such out­puts have been topics for intensive research for the last 4 decades. Several switch­ing strategies realized by modulation techniques have been proposed and tested. As a result, significant contributions on the performance of inverters have been achieved. However, the problem of output harmonic components is still a chal­lenge. One of the most critical limitations of existing modulation techniques is the lack of correlation between these techniques and any inverter models.

An inverter can be modeled as a non-uniform recurrent sampling­ reconstruction process, in which instantaneous switching actions are considered as the reconstruction inverter outputs. This modeling approach can also be employed to verify the effects on inverter outputs due to any changes in the switching strategy. Using the concepts of the sampling theorem, a sampling-reconstruction process is represented as a multiresolution analysis (MRA). Effective and accurate MRAs can be constructed using basis functions generated by scaling and wavelet functions. A modulation technique that incorporates the proposed sampling-based inverter model and a wavelet -based MRA can enable the operation of inverters for high quality outputs. The development, implementation and testing of such a modulation technique is the primary objective of this research.

A novel approach to construct a non-dyadic type MRA that is capable of supporting non-uniform recurrent sampling has been developed. The non-dyadic type MRA is developed based on new scale-based linearly-combined scaling and wavelet functions. The reference-modulating signal is sampled using the new scal­ing function such that a number of sample groups are formed over each cycle of the reference-modulating signal. Each group has two samples that are created by a dilated and translated version of the scaling function. Reconstructing the reference­ modulating signal is carried out by stages of interpolating functions, where each stage is defined over one sample group. This structure of interpolating functions creates one ON switching pulse over each sample group. The approach of operating the inverter aims to concentrate the energy of the output signal in the frequency of the reference-modulating signal. As a result, negligible energy is distributed in the rest of frequency components.

The proposed wavelet modulation technique is implemented using an algorithm for both simulation and experimental testing. The results of both simulations and on-line tests show high quality output voltages and currents indicated by the low values of total harmonic distortion factors. These tests are conducted for different load types under several output frequencies. Also, a new control strategy is developed for adjusting magnitudes and frequencies of wavelet-modulated inverter outputs. This control strategy is called resolution-level control, and is based on changing the scale of the successive reconstruction functions. Simulation and experimental test results of a dc-ac inverter under this control approach demonstrate stable, robust and fast responses for different load changes. The developed non­ dyadic type MRA is extended to operate three-phase inverters. An algorithm is developed for simulation and experimental tests of the three-phase wavelet mod­ulated inverter to supply a R - L load. Results obtained from these tests have demonstrated high quality outputs with negligible harmonic contents.