Mathematical model of power transmission network for calculations in frequency domain

An electrical power transmission networks are one of the most complex modern artificial networks which provides the vital link from generation sources to the distribution networks and presents crucial factor for the security of electricity supply. Harmonic resonance is a phenomenon that occurs when a frequency of external oscillations corresponds with a frequency of self-oscillations, whereby maximum energy is transferred from one oscillating system to another, if their oscillation frequencies are equal or similar. The only way to detect the resonance is to perform calculations by hand or to model the system in special software tool. This work presents procedure for developing a custom mathematical network model for calculations in the frequency-domain and gives an overview of appropriate models of power system components in frequency range of interest. Second part of paper presents possible applications of developed model on real cases, mainly related to cases when large capacitive elements are installed to power systems, for example long cables.