Stochastic field processes in the mathematical modelling of damped transmission line vibrations

Wind-excited vibrations in the frequency range of 10 to 50 Hz due to vortex shedding often cause fatigue failures in the cables of overhead transmission lines. Damping devices, such as the Stockbridge dampers, have been in use for a long time for supressing these vibrations. The dampers are conveniently modelled by means of their driving point impedance, measured in the lab over the frequency range under consideration. The cables can be modelled as strings with additional small bending stiffness. The main problem in modelling the vibrations does however lay in the aerodynamic forces, which usually are approximated by the forces acting on a rigid cylinder in planar flow. In the present paper, the wind forces are represented by stochastic processes with arbitrary crosscorrelation in space; the case of a Kármán vortex street on a rigid cylinder in planar flow is contained as a limit case in this approach. The authors believe that this new view of the problem may yield useful results, particularly also concerning the reliability of the lines and the probability of fatigue damages. © 1987.

A new procedure to derive transmission line parameters: Theoretical considerations

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 the phase currents and voltages in one terminal of the line. First, the article shows the classical methodology to calculate frequency dependent transmission line parameters by using Carson's and Pollaczeck's equations for representing the ground effect and Bessel's functions to represent the skin effect. After that, it is shown a new procedure to calculate frequency dependent transmission line parameters directly from currents and voltages of the line that is already built. Then, this procedure is applied in a two-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. ©2005 IEEE.

Some considerations about a new procedure to derive transmission line parameters concerning three-phase lines

The paper shows an alternative methodology to calculate transmission line parameters per unit length and to apply it in a three-phase line with a vertical symmetry plane. This procedure is derived from a general procedure where the modal transformation matrix of the line is required. In this paper, the unknown modal transformation matrix requested by general procedure is substituted by Clarke's matrix. With the substitution that is shown in the paper, 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 Carson and Pollaczeck's equations for representing the ground effect and Bessel's 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 non-transposed 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 simulation results for typical frequency spectra of switching transients (10 Hz to 10 kHz). Results have shown that procedure has © 2006 IEEE.

Correction procedure applied to a single real transformation matrix -Untransposed three-phase transmission line cases

Clarke's matrix has been used as an eigenvector matrix for transposed three-phase transmission lines and it can be applied as a phase-mode transformation matrix for transposed cases. Considering untransposed three-phase transmission lines, Clarke's matrix is not an exact eigenvector matrix. In this case, the errors related to the diagonal elements of the Z and Y matrices can be considered negligible, if these diagonal elements are compared to the exact elements in domain mode. The mentioned comparisons are performed based on the error and frequency scan analyses. From these analyses and considering untransposed asymmetrical three-phase transmission lines, a correction procedure is determined searching for better results from the Clarke's matrix use as a phase-mode transformation matrix. Using the Clarke's matrix, the relative errors of the eigenvalue matrix elements can be considered negligible and the relative values of the off-diagonal elements are significant. Applying the corrected transformation matrices, the relative values of the off-diagonal elements are decreased. The comparisons among the results of these analyses show that the homopolar mode is more sensitive to the frequency influence than the two other modes related to three-phase lines. © 2006 IEEE.

Corona effect in frequency dependent transmission line models

The inclusion of the corona effect in a frequency dependent transmission line model is proposed in this paper. The transmission line is represented through a cascade of π circuits and the frequency dependence of the longitudinal parameters is synthesized with series and parallel resistors and inductors. The corona effect will be represented using the Gary and Skilling-Umoto models. The currents and voltages along the line are calculated by using state-space technique. To demonstrate the accuracy and validity of the proposed frequency dependent line model, time domain simulations of a 10 km length single-phase line response under energization procedure will be presented. ©2008 IEEE.

A transmission line model developed directly in phase domain

The phases of a transmission line are tightly coupled due to mutual impedances and admittances of the line. One way to accomplish the calculations of currents and voltages in multi-phase lines consists in representing them in modal domain, where its n coupled phases are represented by their n propagation modes. The separation line in their modes of propagation is through the use of a modal transformation matrix whose columns are eigenvectors associated with the parameters of the line. Usually, this matrix is achieved through numerical methods which do not allow the achievement of an analytical model for line developed directly in the phases domain. This work will show an analytical model for phase currents and voltages of the line and results it will be applied to a hypothetical two-phase. It will be shown results obtained with that will be compared to results obtained using a classical model. © 2012 IEEE.

Eigenvalue analyses for non-transposed three-phase transmission line considering non-implicit ground wires

This paper presents a method for analyzing electromagnetic transients using real transformation matrices in three-phase systems considering the presence of ground wires. So, for the Z and Y matrices that represent the transmission line, the characteristics of ground wires are not implied in the values related to the phases. A first approach uses a real transformation matrix for the entire frequency range considered in this case. This transformation matrix is an approximation to the exact transformation matrix. For those elements related to the phases of the considered system, the transformation matrix is composed of the elements of Clarke's matrix. In part related to the ground wires, the elements of the transformation matrix must establish a relationship with the elements of the phases considering the establishment of a single homopolar reference in the mode domain. In the case of three-phase lines with the presence of two ground wires, it is unable to get the full diagonalization of the matrices Z and Y in the mode domain. This leads to the second proposal for the composition of real transformation matrix: obtain such transformation matrix from the multiplication of two real and constant matrices. In this case, the inclusion of a second matrix had the objective to minimize errors from the first proposal for the composition of the transformation matrix mentioned. © 2012 IEEE.

A transmission line model developed directly in phase domain

The phases of a transmission line are tightly coupled due to mutual impedances and admittances of the line. One way to accomplish the calculations of currents and voltages in multi phase lines consists in representing them in modal domain, where its n coupled phases are represented by their n propagation modes. The separation line in their modes of propagation is through the use of a modal transformation matrix whose columns are eigenvectors associated with the parameters of the line. Usually, this matrix is achieved through numerical methods which do not allow the achievement of an analytical model for line developed directly in the phases domain. This work will show an analytical model for phase currents and voltages of the line and results it will be applied to a hypothetical two-phase. It will be shown results obtained with that will be compared to results obtained using a classical model © 2003-2012 IEEE.

A distributed-parameters transmission line model developed directly in the phase domain

This article shows a transmission line model developed directly in the phase domain. The proposed model is based on the relationships between the phase currents and voltages at both the sending and receiving ends of a single-phase line. These relationships, established using an ABCD matrix, were extended to multi-phase lines. The proposed model was validated by using it to represent a transmission line during short-and open-circuit tests. The results obtained with the proposed model were compared with results obtained with a classical model based on modal decomposition. These comparisons show that proposed model was correctly developed. © 2013 Taylor and Francis Group, LLC.

Fitting the frequency-dependent parameters in the Bergeron line model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Tap-Off Power From the Overhead Shield Wires of an HV Transmission Line

In recent years, there was an increase of ancillary service loads, such as signaling systems, inspection robots, surveillance cameras, and other monitoring devices distributed along high-voltage transmission lines which require low-power dc voltage supplies. This paper investigates the use of the induced voltage in the shield wires of an overhead 525 kV transmission line as a primary power source. Since phase current variations throughout the day affect the induced voltage in the overhead ground wire, a step-down dc-dc converter is used after rectification of the ac voltage to provide a regulated dc output voltage. The initial encouraging results obtained indicate that this form of power supply can be a feasible and cost-effective alternative for feeding small ancillary service loads. The simulation results are validated by field measurements as well as the installation of a 200 W voltage stabilization system prototype.

Malin-Warner 230 kV transmission line construction (OR,CA), environmental assessment (EA), Finding of no significant impact (FONSI).

Mode of access: Internet.

Environmental assessment using remotely sensed data : application of remote sensing data to environmental impact studies for transmission line routes /

Mode of access: Internet.

Design considerations for multilayer transmission line circuit boards.

Issued also as thesis (M.S.) University of Illinois.

An application of intercoupled-transmission-line-amplifier /

"November 1, 1965."