General harmonic families elimination methodology for static converters control

The harmonic families elimination concept, already introduced in previous papers, presents some interesting advantages with respect to the single-components approach that is adopted for the classic harmonic elimination techniques. In fact, this more restrictive approach allows analytic explicit solutions to be obtained with a lower computational effort, permitting implementations having a lower complexity and cost with respect to the classic techniques. In this paper, the harmonic families elimination problem is formulated and approached in general theoretical terms, demonstrating the possibility to translate it from the initial integral form, referred to the Fourier coefficients, into a simpler algebraic functional problem directly referred to the waveform, corresponding to impose to it particular structural properties named “n-symmetries”. By showing that this second problem can also be translated in a conceptually very simple linear algebraic nonfunctional form, it is then deduced that the general solution of the problem can be expressed as a suitable linear combination of some subfunctions acting as free parameters, whose waveform can be chosen arbitrarily. Considerations are also developed about the particular properties of the problem and the practical difficulties correlated to the direct numerical calculation of the solution matrix. A few numerical results are finally reported for some solved cases, both in general terms and as application to the control of inverters