Using the Exact Equivalent π-Circuit of Transmission Lines for Electromagnetic Transient Simulations in the Time Domain

Abstract

This work presents a transmission line model for simulating electromagnetic transients directly in the time domain. For this purpose, the exact equivalent π-circuit is used, which represents the line taking into account its distributed and frequency-dependent parameters. The admittances that constitute the exact equivalent π-circuit are approximated by rational functions using the vector fitting technique. Then, for each admittance, an electrical circuit is synthesized, consisting of an association of discrete elements (resistors, inductors, and capacitors) aiming at modeling the transmission line, thus allowing its use in any circuit simulation software and the eventual connection of nonlinear elements. From the simulation results, it is reasonable to state that the proposed model is a feasible representation, which aggregates the same features of the exact equivalent π-circuit directly in the time domain, not only in steady state, but mainly during transients and also without the need for using convolutions, as well as inverse Laplace or Fourier transforms.INDEX TERMS Electromagnetic transients, Transmission line model, Time-domain analysis, Vector Fitting.

Using the Exact Equivalent π-Circuit Model for Representing Three-Phase Transmission Lines Directly in the Time Domain

“…However, this model can only be represented in the frequency domain [35]. Its representation in the time domain was recently proposed in [29]. This approach relies on the synthesis of the admittance curves of Y zπ and Y π of the equivalent π-circuit, as shown in Figure 1; furthermore, this is achieved using only passive elements like resistors, inductors, and capacitors.…”

“…In this context, the authors in [29] presented a new single-phase TL model that was developed directly in the time domain, which considers the TL's pul parameters and the frequency effect. The model synthesizes the exact equivalent π-circuit of the TL using an electrical circuit composed of an association of discrete elements (resistors, inductors, and capacitors).…”

“…It is also known as the "long π" model as it represents a long-distance line using a single π-circuit [32], or simply an π-circuit equivalent representation [33]. In this way, by using the equivalent π-circuit directly in the time domain, the authors in [29] overcame some of the limitations of the aforementioned models. This is because the proposed approach allows for the simulation of electromagnetic transients directly in the time domain, and this is achieved without the prior calculation of the delay time τ, as well as without the use of inverse Laplace or Fourier transforms.…”

“…Given the above, the primary goal of this paper is to use the model developed in [29] to represent the symmetrical and ideally transposed three-phase TLs. The procedure is carried out using modal transformation, which allows for the decomposing of the three-phase TL into three propagation modes, each of which behave as an independent single-phase line [34].…”

Electromagnetic Transient Simulation Algorithm for Nonlinear Elements Based on Rosenbrock Numerical Integration Method

“…Reference [28] used z-transform to achieve electromagnetic transient simulation of transmission lines in the frequency domain, but it cannot be used for power systems containing nonlinear lumped parameter components [29]. Reference [30] proposed time-domain EMT simulations for transmission lines with variable frequency parameters, and this method is also applicable to simulation of circuit systems with nonlinear load components. The above methods are applicable in avoiding numerical oscillation problems, but there are still some unresolved issues for EMT simulations of largescale power systems containing nonlinear components.…”