On Dynamic Evaluation of Harmonics Using Generalized Averaging Techniques

Two distinct methods of applying generalized averaging techniques appear in the literature. The first method involves a direct mathematical mapping of all system equations and inputs into the frequency domain to produce harmonic coefficients that precisely match those produced by a sliding window Fourier decomposition during transient events. Although this approach reproduces the same harmonic coefficients as a sliding window decomposition, it is shown that reconstruction of the time domain waveforms does not match the response of the underlying time domain system during transients. In contrast, a second method has recently been employed by some researchers that does not strictly map all system equations and inputs into the frequency domain, and yet it has been shown to precisely reproduce time domain results during transients. This paper shows that this matching of the time domain transients comes at the expense of introducing spurious dynamics into the associated harmonic domain model, which may not exist in the underlying time domain system. The limitations and implicit assumptions behind these two methods are identified and compared, thus allowing researchers to readily determine which compromises are to be made based on the application in question.