Application of the State Variables Method on Quickly Evaluation of the Harmonic Resonance Frequencies in a Transmission Line

The harmonics propagation in a power network is directly influenced by the value of the equivalent harmonic impedance (seen) in each section of the network. The state variable method, initially applied for the automated systems study, has many other applications. One of them, presented in this paper, consists in a quick determination of the frequencies for which the harmonic impedance, as seen from a power network bus, exhibits poles (maximums - corresponding to parallel resonance) and zeroes (minimurns -corresponding to series resonance). The comparison of these frequencies with those of the harmonic currents - present in the network - allows a quick evaluation of the harmonics amplifying risk. The paper also presents the results of applying this method at the evaluation of the harmonic resonance frequencies on a transmission line, results later compared with those obtained with a classical method -the inversion of the network admittance matrix.