On the Solution of Transcendental Eigenvalue Problem in Transmission Line Bundled Conductors

2004 ◽  
Author(s):  
Himanshu Verma ◽  
Ashish M. Dighe ◽  
Peter Hagedorn
Keyword(s):  
Energy Balance ◽  
Eigenvalue Problem ◽  
Transmission Line ◽  
Transmission Lines ◽  
Input Data ◽  
Natural Frequencies ◽  
Standard Form ◽  
Electrical Transmission ◽  
Energy Balance Method ◽  
New Approach

Overhead electrical transmission lines are always susceptible to aeolian vibrations, caused by light to moderate winds. Spacer dampers are used in bundled transmission lines to keep the conductors at required minimum spacing and to suppress the wind induced vibrations. Mathematical models are necessary for the computation of the conductor vibrations for studying the efficiency of damping measures. The so called energy balance method gives good results for estimating the vortex excited vibrations of overhead electrical transmission lines. In its standard form it requires the knowledge of the eigenfunctions, which are routinely calculated for the single conductor lines. However, the problem becomes more involved in the case of bundled conductors with spacer dampers due to very dense spectrum of the natural frequencies. In the present paper some approaches towards solving the transcendental eigenvalue problem (EVP) for the bundled conductors with spacer dampers are discussed. It is formulated as an algebraic transcendental EVP, which however presents several numerical difficulties. Reasons for these numerical difficulties are discussed in some detail. A new approach, named as “continuous spectrum approach,” provides better engineering solution for the transmission line bundled conductors. The solution of the EVP gives the necessary input data for applying the energy balance.

scholarly journals On Heaviside's contributions to transmission line theory: waves, diffusion and energy flux

2018 ◽  
Vol 376 (2134) ◽  
pp. 20170457
Author(s):  
Christopher Donaghy-Spargo
Keyword(s):  
Transmission Line ◽  
Transmission Lines ◽  
Physical Nature ◽  
Electromagnetic Theory ◽  
Electrical Transmission ◽  
Important Work ◽  
Transmission Line Theory ◽  
Energy Current ◽  
Electrical Transmission Line ◽  
Line Theory

This paper surveys some selected contributions of Oliver Heaviside FRS (1850–1925) to classical electromagnetic theory and electrical engineering science. In particular, the paper focuses on his contributions to the development of electrical transmission line theory and his deep insights into the ‘physical’ nature of the phenomena relating to nineteenth century telegraphic problems. Following a brief historical introduction to the life of Heaviside to put his achievements in context, we explore his contributions to the reformulation of Maxwell's equations and the understanding of electromagnetic wave propagation along the external region of transmission lines. This leads naturally to his researches regarding the electromagnetic diffusion process inside the line conductors and his subsequent realization that the circuital parameters, usually assumed constant, are not always so. Finally, taking both these internal and external viewpoints of the conductors, his important work regarding the flow of energy described by his ‘energy current’ concept is presented. This article is part of the theme issue ‘Celebrating 125 years of Oliver Heaviside's ‘Electromagnetic Theory’’.

scholarly journals Analogue Hawking Radiation in Nonlinear LC Transmission Lines

Universe ◽  
2021 ◽  
Vol 7 (9) ◽  
pp. 334
Author(s):  
Haruna Katayama ◽  
Noriyuki Hatakenaka ◽  
Ken-ichi Matsuda
Keyword(s):  
Black Holes ◽  
Electromagnetic Wave ◽  
Transmission Line ◽  
Transmission Lines ◽  
Hawking Radiation ◽  
Reductive Perturbation Method ◽  
Electrical Transmission ◽  
Third Order ◽  
Nonlinear Transmission Lines ◽  
Electrical Transmission Line

Analogue systems are used to test Hawking radiation, which is hard to observe in actual black holes. One such system is the electrical transmission line, but it suffers the inevitable issue of excess heat that collapses the successfully generated analogue black holes. Soliton provides a possible solution to this problem due to its stable propagation without unnecessary energy dissipation in nonlinear transmission lines. In this work, we propose analogue Hawking radiation in a nonlinear LC transmission line including nonlinear capacitors with a third-order nonlinearity in voltage. We show that this line supports voltage soliton that obeys the nonlinear Schrödinger equation by using the discrete reductive perturbation method. The voltage soliton spatially modifies the velocity of the electromagnetic wave through the Kerr effect, resulting in an event horizon where the velocity of the electromagnetic wave is equal to the soliton velocity. Therefore, Hawking radiation bears soliton characteristics, which significantly contribute to distinguishing it from other radiation.

scholarly journals In-Cloud Icing in the Columbia Basin

2009 ◽  
Vol 137 (12) ◽  
pp. 4369-4381 ◽  
Author(s):  
Ronald M. Thorkildson ◽  
Kathleen F. Jones ◽  
Maggie K. Emery
Keyword(s):  
Transmission Line ◽  
Water Content ◽  
Transmission Lines ◽  
Liquid Water ◽  
Liquid Water Content ◽  
Weather Data ◽  
Cloud Base ◽  
Columbia Basin ◽  
Electrical Transmission ◽  
Dewpoint Temperature

Abstract On 24 November 2005, 11 lattice steel towers of a high-voltage electrical transmission line running along the edge of an escarpment were damaged by an accumulation of rime on overhead ground wires. Cold air pooling in the Columbia basin of eastern Washington several days before the failure led to the formation of low-level fog and low clouds with temperatures below freezing at the elevation of the transmission line. The liquid water content profile of the cloud formed by air rising over Badger Mountain north of Wenatchee, Washington, is estimated using the air temperature, dewpoint temperature, and air pressure as measured at Wenatchee in the Columbia River valley below the line. Cloud median volume droplet diameters are estimated using typical droplet concentrations. The validity of the computed liquid water content is determined by comparing the measured cloud-base heights at Wenatchee with the calculated cloud-base heights. The mass and density of ice accreted on the ground wires and conductors of the transmission line are modeled using assumed wind speeds at the top of the escarpment with the estimated cloud properties. Results are compared with the density and mass of an ice sample retrieved from the field. This event is compared with other modeled in-cloud icing events from 1973 to 2007 using the period of record of Wenatchee weather data. This paper illustrates an approach for estimating the severity of in-cloud icing on the wires of transmission lines subject to cloud liquid water contents that have been enhanced by the local terrain.

scholarly journals Note on surges of voltage and current in transmission lines

1936 ◽  
Vol 156 (887) ◽  
pp. 1-5 ◽  
Keyword(s):  
Transmission Line ◽  
Transmission Lines ◽  
Subject Matter ◽  
Unit Length ◽  
The Self ◽  
Practical Calculation ◽  
Electrical Transmission ◽  
Present Treatment ◽  
Distant Point ◽  
The Subject

The increase in extent and capacity of electrical transmission systems lends increasing importance to the subject matter of this note; for excessive survoltage, particularly when it occurs suddenly, is apt to damage equipment and endanger life, cause a large and virtually instantaneous rise of potential at the point struck; and it is important, in the study of its effects, to determine the resulting disturbance at a distant point of the line. A solution of the fundamental case of an infinite transmission line, at the end of which a change of potential suddenly occurs, was propounded by Heaviside, but this solution appears to be incorrect. It nevertheless seems to have been very generally accepted by engineers who have dealt with the problem. The subject has also been discussed by Jeffreys, but it is felt that the present treatment offers advantages, not only in that it leads to a clearer physical apprehension of the phenomena, but also as being more amenable to the purpose of practical calculation. The equations between voltage V and current i at any point x and time t are d V/ dx + L di / dt + R i = 0, (1) di / dx + K d V/ dt + SV = 0, (2) where R is the resistance, S the leakage conductance, L the self-induction, and K the capacity of the line-all reckoned per unit length. Whence, d 2 V/ dx 2 = LK d 2 V/ dt 2 + (RK + SL) d V/ dt +RSV. (3)

Analytical Solutions for Nonlinear Lateral Sloshing in Partially-Filled Elliptical Tankers

2011 ◽  
Author(s):  
Davood Younesian ◽  
Hassan Askari ◽  
Zia Saadatnia ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Dynamical System ◽  
Energy Balance ◽  
Analytical Solution ◽  
Free Oscillation ◽  
Natural Frequencies ◽  
Nonlinear Dynamical System ◽  
Solution Technique ◽  
Initial Amplitude ◽  
Energy Balance Method ◽  
Nonlinear Dynamical

Dynamic behavior of the large amplitude lateral sloshing is analytically studied in partially filled elliptical tankers. Theory of elliptical trammel pendulums is employed for modeling of the large oscillation of the fluid inside the elliptical container. Nonlinear governing equation of the motion is derived employing the Hamilton principle. Standard and modified Energy Balance Method (EBM) is adopted as the solution technique. Natural frequencies of the free oscillation are analytically obtained as a function of the initial amplitude. It is proved that the nonlinear dynamical system can behave mutually as a hardening and softening system based on the tanker aspect ratio. A number of numerical simulations are carried out and accuracy of the obtained analytical solution is evaluated.

HIGHER-ORDER ENERGY BALANCE METHOD FOR A SERIES OF NONLINEAR OSCILLATORY SYSTEMS

2013 ◽  
Vol 06 (04) ◽  
pp. 1350054 ◽  
Author(s):  
Z. Saadatnia ◽  
N. Safaie ◽  
M. A. Ahmadpour ◽  
H. Askari
Keyword(s):  
Energy Balance ◽  
Natural Frequencies ◽  
Initial Conditions ◽  
Nonlinear Problems ◽  
Solution Procedure ◽  
Higher Order ◽  
Balance Method ◽  
Energy Balance Method ◽  
Oscillatory Systems ◽  
Order Energy

The aim of this paper is to use higher-order energy balance method as a novel solution procedure for investigation the nonlinear oscillation of various systems. The method is associated with collocation method and employed for a group of nonlinear problems including pure cubic nonlinearity, fractional elastic force and duffing harmonic terms. Obtained results are evaluated by comparing with the classical balance method and also the exact solutions computed numerically. It is shown our solution procedure achieves more accurate results versus the classical solution and higher agreement are observed between the newer solutions and the exact ones for the systems. Effect of initial conditions in the nonlinear natural frequencies are carried out for a range of small and large values and it is proved the proposed method is not only simple but also more reliable for analysis of such systems.

scholarly journals Design aspects of high voltage transmission line

2020 ◽  
Vol 9 (3) ◽  
pp. 853-861
Author(s):  
Jabbar Qasim Fahad ◽  
Riyadh Kamil Chillab
Keyword(s):  
Transmission Line ◽  
Transmission Lines ◽  
Electrical Power ◽  
Implementation Process ◽  
Overhead Line ◽  
Electrical Transmission ◽  
High Voltage Transmission Line ◽  
High Tension ◽  
Electrical Transmission Line ◽  
Selection Of

The transmission lines are very important in the transmitted of electrical power, and the process of selecting the voltage of the line is an important task in the design and implementation process. The process of transferring electrical power from one side then onto the next place for long away. While maintaining the percentage regulation within the permissible limits is an important problem in the transfer of energy. In electrical transmission line there are important elements are resistance, inductance and capacitance. The purpose of this paper is to study and calculate economic high-tension voltage and selection of overhead line conductor ACSR.

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