An algorithm for fitting passive equivalent circuits for lumped parameter frequency dependent transmission line models

Abstract

Accurately fitting rational functions to the frequency response of modal impedances is crucial for including frequency dependency in lumped parameter models of transmission lines. Vector fitting is widely used for fitting rational functions to the frequency response of modal impedances and then an R-L equivalent circuit is obtained from the rational functions. A single-step method based on the properties of Foster equivalent circuit is proposed to directly fit an R-L equivalent circuit to the frequency response of modal impedances. The positive peaks, negative peaks and the positive zero crossings of the slope change plot of the frequency response are found to provide a good approximation of zeros, poles and the flat region locations of the frequency response. An enhanced fitting algorithm is proposed based on these observations. A close enough fitting is achieved using the proposed method with less number of passive elements. Using the proposed model in EMTP-RV, 400, 765, 1200 kV transmission lines and a 11-bus 500 kV network are simulated for switching transients. The results are compared with the constant parameter cascaded-model and the Frequency-dependent line model in EMTP-RV. The switching transient results of the proposed model are found to be comparable to the Marti's model in EMTP-RV.

Analytical formulas for calculating the electrical characteristics of multiparameter arbitrary configurational homogenous ladder networks

“…They are passive electrical circuits formed by series and parallel impedances with repetition of elementary sections. For instance, photo‐electrochemical cells, 1 respiratory tissues, 2 humidity sensors, 3 electrochemical polarisation, 4 transformers, 5 transmission lines 6 and photovoltaic cells 7 are all examples. Thus, it is an interdisciplinary problem to compute electrical characteristics like voltages, currents and driving point impedance () for any complex ladder network with RLCG parameters.…”