Proposal of a Transmission Line Model Based on Lumped Elements: An Analytic Solution

Abstract

This article proposes a frequency-dependent transmission line model based on state-space techniques. To include the frequency effect associated with distributed parameters in the state matrices, the line frequency-dependent longitudinal parameters are fitted by a rational function and then introduced in lumped elements representation by an equivalent RL circuit; this procedure is known as vector fitting. Subsequently, the system of ordinary differential equations that represents the transients of currents and voltages on a three-phase transmission line is represented in state space. After the state equations are solved by numerical and analytic methods, the results are compared to a frequency-dependent lumped model implemented by the commercial software MICROTRAN (an electromagnetic transient program; Microtran Power Systems Analysis Corporation, Vancouver, Canada). Following this, the results obtained from the proposed lumped model are compared to results from a distributed-parameters model based on Fourier transform. Some of the principal advantages for using the proposed state-space model instead of a distributed-parameters modeling are the easy modeling of several electromagnetic phenomena over transmission lines directly in the time domain without the use of inverse transforms and that a detailed description of the voltages and currents along the line can be described with good approximation. These attributes are not observed for models based on distributed parameters. All simulations are performed considering the switching operation of a 440-kV three-phase line, and by this procedure, it is possible to analyze the accuracy of the proposed line modeling.