Generalized fourier series - a useful mathematical tool in power electronics

The paper is related to the problem of creating stepped waveforms by use the generalized Fourier series. This method can be applied especially in power electronics as a tool permitting to reach AC voltage waveforms approximated to the sine wave shape. This novel approach to the synthesis of AC voltage waveforms is based on Fourier series of orthogonal functions set. Applying analytical methods and expressions given in the paper it is possible to define such optimal parameters of the waveform in order to receive the lowest harmonics content. The presented mathematical tool is very useful in designing structures and control algorithms of multilevel converters.