The L1-impulse method as an alternative to the Fourier series in the power theory of continuous time systems

The Fourier series method is frequently applied to analyze periodical phenomena in electric circuits. Besides its virtues it has many drawbacks. Fourier series usually have slow convergence and fail for fast changing signals, especially for discontinues ones. Therefore they are suitable to describe only quasiharmonic phenomena. For strongly nonsinusoidal signal analysis we propose the L1-impulse method. The L1-impulse method consists in an equivalent notation of a function belonging to L1 as a sum of exponential functions. Such exponential functions have rational counterparts with poles in both sides of imaginary axis. With the L1-impulse functions we can describe periodical signals, thus we get the homomorfizm between periodical signals and a rational functions sets. This approach is especially adapted to strongly deformed signals (even discontinues ones) in linear power systems, and thanks to that we can easily calculate optimal signals of such systems using the loss operator of the circuit. The loss operator is exactly the rational function with central symmetry of poles [1]. In this paper the relation between the L1-impulse and the Fourier series method was presented. It was also proved that in the case of strong signal deformation the L1-impulse method gains advantage.