J. Pissolato

A new procedure to derive transmission-line parameters: applications and restrictions

The objective of this paper is to show an alternative methodology to calculate transmission-line parameters per unit length. With this methodology, the transmission-line parameters can be obtained starting from impedances measured in one terminal of the line. First, the article shows the classical methodology to calculate frequency-dependent transmission-line parameters by using Carsons and Pollaczecks equations for representing the ground effect and Bessels functions to represent the skin effect. After that, a new procedure is shown to calculate frequency-dependent transmission-line parameters directly from currents and voltages of an existing line. Then, this procedure is applied in a two-phase and a three-phase transmission line whose parameters have been previously calculated by using the classical methodology. Finally, the results obtained by using the new procedure and by using the classical methodology are compared. The article shows simulations results for a typical frequency spectrum of switching transients (10 Hz to 10 kHz).

Quasi-modes three-phase transmission line model—transformation matrix equations

Abstract This paper describes the quasi-modes three-phase transmission line model, a new model to represent three-phase transmission lines in transient studies, with proper representation of the frequency dependence of longitudinal parameters. A unique transformation matrix—the Clarke matrix—is used for the entire frequency range. As this matrix is a real one. it can be modeled through ideal transformers. The circuit equations, which lead to the matrix modeling, are presented. This line model can be implemented in any digital program with R , L , C and transformer components.

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.

Alternative proposal for Modal Representation of a Non-transposed Three-Phase Transmission Line with a Vertical Symmetry Plane

The objective of this paper is to show an alternative representation in time domain of a non-transposed three-phase transmission line decomposed in its exact modes by using two transformation matrices. The first matrix is Clarkes matrix that is real, frequency independent, easily represented in computational transient programs (EMTP) and separates the line into quasi-modes a, b and zero. After that, Quasi-modes a and zero are decomposed into their exact modes by using a modal transformation matrix whose elements can be synthesized in time domain through standard curve-fitting techniques. The main advantage of this alternative representation is to reduce the processing time because a frequency dependent modal transformation matrix of a three-phase line has nine elements to be represented in time domain while a modal transformation matrix of a two-phase line has only four elements. This paper shows modal decomposition process and eigenvectors of a non-transposed three-phase line with a vertical symmetry plane whose nominal voltage is 440 kV and line length is 500 km.

Representação de linhas de transmissão por meio de variáveis de estado levando em consideração o efeito da freqüência sobre os parâmetros longitudinais

The main objective of this paper is to show the formulation rule of state matrices when the state-space approach is used to represent a transmission line taking into account its frequency dependent parameters. First, the line is represented through a cascade of p circuits and the frequency dependence of the longitudinal parameters is synthesized with series and parallel resistors and inductors that are inserted in each p circuit. After that the cascade is described through state equations. The model will be used to represent a single-phase line taking into account that its parameters are frequency dependents. The simulations are carried out by using Matlab and the results obtained will be compared with results obtained with Microtran.

An Alternative Modal Representation of a Symmetrical Nontransposed Three-Phase Transmission Line

The objective of this letter is to propose an alternative modal representation of a nontransposed three-phase transmission line with a vertical symmetry plane by using two transformation matrices. Initially, Clarkes matrix is used to separate the line into components alpha,beta, and zero. Because alpha and zero components are not exact modes, they can be considered as being a two-phase line that will be decomposed in its exact modes by using a 2times2 modal transformation matrix. This letter will describe the characteristics of the two-phase line before mentioned. This modal representation is applied to decouple a nontransposed three-phase transmission line with a vertical symmetry plane whose nominal voltage is 440kV

Quasi-modes three-phase transmission line model — comparison with existing frequency dependent models☆

Abstract This paper presents a new model to represent multiphase transmission lines in transient studies, including the frequency dependence of longitudinal parameters. The frequency dependence is represented with synthetic circuits, with a cascade of π-circuit for each mode. A real transformation matrix is used for the entire frequency range and it is modeled through ideal transformers in a transient program like ATP, as described. An application of the methodology is presented for an actual 440 kV single three-phase transmission line where some transients results simulated in ATP are presented. The model is compared to two ATP line models, JMarti and Semlyen.

New mode-domain representation of transmission line-Clarke transformation analysis

This paper presents a new model to represent multiphase transmission lines in transient studies, including the frequency dependence of longitudinal parameters. The frequency dependence is represented with synthetic circuits, with a cascade of /spl pi/-circuits for each mode. The transformation matrix used for the entire frequency range is the Clarke one. The model is described for three-phase lines. The exact eigenvector of the non-transposed line is analyzed in the frequency domain for some earth resistivity and compared to Clarke components.

Integration Methods Used in Numerical Simulations of Transient Electromagnetic

This paper made an analysis of some numerical integration methods that can be used in electromagnetic transient simulations. Among the existing methods, we analyzed the trapezoidal integration method (or Heun formula), Simpsons Rule and Runge-Kutta. These methods were used in simulations of electromagnetic transients in power systems, resulting from switching operations and maneuvers that occur in transmission lines. Analyzed the characteristics such as accuracy, computation time and robustness of the methods of integration.

A Model for Bundled Conductors Considering a Non-Homogeneous Distribution of the Current through Subconductors

This paper describes an alternative procedure to obtain an equivalent conductor from a bundled conductor, taking into account the distribution of the current in subcondutors of the bundle. Firstly, it is introduced a brief background about the concept of Geometric Mean Radius (GMR) and how this methodology is applied to define an equivalent conductor and its electric parameters. Emphasizing that the classical procedure, using GMR, is limited to premise which the current is equally distributed through subconductors. Afterwards, it is described the development of proposed method and applications for an equivalent conductor obtained from a conventional transmission line bundled conductor and from an equivalent conductor based on a bundle with compressed SF6 insulation system, where the current is unequally distributed through subconductors.