Optimization of Lumped Parameter Models to Mitigate Numerical Oscillations in the Transient Responses of Short Transmission Lines

Colqui, Jaimis Sajid León; Araújo, Anderson Ricardo Justo de; Kurokawa, Sérgio; Filho, José Pissolato

doi:10.3390/en14206534

Cited by 5 publications

(5 citation statements)

References 18 publications

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“…Comparing the coefficients of V B and I B in ( 1) and ( 7), one can obtain ( 9) and (10), which correspond to the admittances Y zπ and Y π of the equivalent π-circuit shown in Figure 2.…”

Section: Exact Equivalent π-Circuit Of Tlsmentioning

confidence: 99%

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

2022

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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.

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Section: Exact Equivalent π-Circuit Of Tlsmentioning

confidence: 99%

“…To reduce the spurious oscillations, in [8] damping resistances are added in parallel with the longitudinal impedance of each section of the nominal π-circuit. Later on in [9], [10], a methodology was presented to better adjust the damping resistance values in order to reduce the transient response distortion.…”

Section: Introductionmentioning

confidence: 99%

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

2022

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“…Articles [12,13] present mathematical models of a power line involving cascades of equivalent linear circuits connected in series and taking into account complex line parameters. The electromagnetic state of each cascade is described by first-order ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

Including Shield Wires in the Analysis of Transient Processes Occurring in HVAC Transmission Lines

Chaban,

Popenda,

Szafraniec

et al. 2023

Energies

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The article presents an analysis of electromagnetic transient processes in long ultra-high voltage transmission lines, taking into account shield wires. It was shown that EMTP and Matlab/Simulink software are currently widely used in the study of transient processes in power lines. The EMTP software package uses the finite element method when integrating the equation that mathematically models the distributed parameter transmission line. The Matlab/Simulink software uses the d’Alembert method. In both cases, it is not known how the boundary conditions for the partial differential equation that mathematically models the transmission line are determined. The power line is analyzed as a distributed parameter system, described by a second-order partial differential equation. The advantage of the proposed method of calculating the boundary conditions for the abovementioned equation is the use of boundary conditions of the second and third types of Neumann and Poincaré, which allowed us to take into account the mutual influence of shield wires and phase conductors of the line in one power system. On this basis, the methodology for obtaining time domain graphs, spatial distributions, and traveling wave distributions of voltages and currents for phase conductors and line shielding wires is presented. The results of a computer simulation of transient processes when switching on the power line, taking into account controlled phase commutation and under single-phase earth fault conditions, are presented. All calculation results of transient processes presented in the article were obtained exclusively using numerical methods.

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“…Articles [7,8] introduce supply line mathematical models that include cascades of equivalent line circuits in series which address complicated line parameters. The electro-magnetic state of each cascade is described with ordinary first-order differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…However, these approaches require well-defined boundary conditions regarding the long transmission line equation [3,[13][14][15]. The conditions were determined using analytical integration [2] or equivalent substitutions [7][8][9][10]. Concerning the MatLab software package, the distributed line model built into the Simulink library was also simplified.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Transient Processes in a Three Phase Electric Power System for a Single Phase Short-Circuit

et al. 2022

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Field approaches are employed to develop a mathematical model of a power network section. The facility consists of two electric power subsystems described with ordinary differential equations and presented as concentrated parameter systems connected with a three-phase power supply line, presented as a distributed parameter system. The model of the electric power line is described with partial differential equations. Mathematically, the supply line model is described utilizing a mixed problem with explicitly indefinite boundary conditions. All electromagnetic state equations of the integrated system are introduced in their matrix-vector forms. The equation of the three-phase long supply line is expressed untraditionally as a system of two first-order differential equations as a function of long line voltage. Since the power supply line is part of the integrated system that includes two subsystems, the boundary conditions at the line's start and end are implicitly defined, avoiding the traditional application of the Dirichlet first-type boundary condition. An expanded system of ordinary differential equations that describe physical processes in both the supply and loading subsystems is used to calculate the boundary conditions. To this end, third-type boundary conditions, or Poincaré's conditions, serve to describe the wave equation of the electric power line. Such an integrated model of an electric power system helps analyse transient processes across the supply line when the electric power system is switched on and is single-phase short-circuited at the final point of the electric power line. A comparison of computer simulation results with well-known software packages shows a convergence of approx. 96%.

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Optimization of Lumped Parameter Models to Mitigate Numerical Oscillations in the Transient Responses of Short Transmission Lines

Cited by 5 publications

References 18 publications

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

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

Including Shield Wires in the Analysis of Transient Processes Occurring in HVAC Transmission Lines

Mathematical Modelling of Transient Processes in a Three Phase Electric Power System for a Single Phase Short-Circuit

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