This thesis proposes an analytical method based on three-dimensional Fourier integral to obtain accurate spectra of both the switching functions and the synthesized output voltages and input currents of matrix converter. The principle of this analytical is carried out in two steps. The first step is that the spectra of the switching functions are derived based on three-dimensional Fourier integral. The second step is that the spectra of the output voltages and input currents are evaluated using a convolution operation in the frequency domain. The challenges associated with the spectral analysis of matrix converter waveforms are twofold. On one hand, the modulation signal contains both the input and output frequencies. Unlike the third harmonic injection in the modulation functions, the input frequency and the output frequency are typically independent from each other and will not form an integer ratio. On the other hand, it is very common that the switching frequency or the carrier frequency is not rational multiple of either the input frequency or the output frequency. These aforementioned challenges make it a very challenge task to accurately characterize the spectra of matrix converter waveforms through commonly resorted numerical methods such as fast Fourier transform (FFT). The proposed analytical approach, which is an extension of the double Fourier series expansion for the pulse width modulated waveforms of voltage source inverter will provide an accurate solution to spectral analysis of matrix converters.
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