Simulation of complex‐valued, frequency‐dependent quantities in transients programs

Transients analysis in power systems requires for many applications an effective and accurate simulation of complex‐valued, frequency‐dependent quantities, e. g. the simulation of grounding structures. The objective of this paper is to give methods to represent complex‐valued, frequency‐dependent quantities by adequate functions and strategies to incorporate them in transients programs. This shall be done in a general manner, without focusing on a specific application. Due to the fact, that transients programs work in the time domain, methods performing the transformation from the frequency into the time domain during the run‐time simulation are mandatory. The methodology to fit the frequency response by means of rational functions is well known. In the first part methods to incorporate rational functions into transients programs are briefly introduced. In the second part three different approaches to determine accurate approximations of complex‐valued, frequency‐dependent quantities are presented. Afterwards the different strategies are tested and discussed with regard to different applications. Finally, the incorporation is validated by comparison to Fast Fourier Transform (FFT).