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.

Development of a simplified transmission line model directly in the phase domain

A transmission line digital model is developed direct in the phase and time domains. The successive modal transformations considered in the three-phase representation are simplified and then the proposed model can be easily applied to several operation condition based only on the previous knowing of the line parameters, without a thorough theoretical knowledge of modal analysis. The proposed model is also developed based on lumped elements, providing a complete current and voltage profile at any point of the transmission system. This model makes possible the modeling of non-linear power devices and electromagnetic phenomena along the transmission line using simple electric circuit components, representing a great advantage when compared to several models based on distributed parameters and inverse transforms. In addition, an efficient integration method is proposed to solve the system of differential equations resulted from the line modeling by lumped elements, thereby making possible simulations of transient and steady state using a wide and constant integration step. © 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.

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.

Graded Meshes In Bio-thermal Problems With Transmission-line Modeling Method.

In this study, the transmission-line modeling (TLM) applied to bio-thermal problems was improved by incorporating several novel computational techniques, which include application of graded meshes which resulted in 9 times faster in computational time and uses only a fraction (16%) of the computational resources used by regular meshes in analyzing heat flow through heterogeneous media. Graded meshes, unlike regular meshes, allow heat sources to be modeled in all segments of the mesh. A new boundary condition that considers thermal properties and thus resulting in a more realistic modeling of complex problems is introduced. Also, a new way of calculating an error parameter is introduced. The calculated temperatures between nodes were compared against the results obtained from the literature and agreed within less than 1% difference. It is reasonable, therefore, to conclude that the improved TLM model described herein has great potential in heat transfer of biological systems.

Erweiterung der Transmission-Line-Methode auf die Biegewelle zur Simulation von Crashsensorsignalen

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2011

Microwave Slot Transmission Line Filled with Ferroelectric and Ferromagnetic Layers

Now when the technology is fast developing it is very important to investigate new hybrid structures. One way is to use ferrite ferroelectric layered structures. Theoretical and experimental investigation of such structures was made. These structures have advantages of both layers and it is possible to tune the behavior of this structure by external electric and magnetic field. But these structures have some disadvantages connected with presence of thick ferroelectric layer. One way to overcome this problem is to use slotline. So this is another new way to create hybrid ferrite ferroelectric structures, but it is needed to create new theory and find experimental proof that the behavior of these structures can be tuned with external magnetic and electric fields.

Avian mortalities due to transmission line collisions: a review of current estimates and field methods with an emphasis on applications to the Canadian electric network

Birds are vulnerable to collisions with human-made fixed structures. Despite ongoing development and increases in infrastructure, we have few estimates of the magnitude of collision mortality. We reviewed the existing literature on avian mortality associated with transmission lines and derived an initial estimate for Canada. Estimating mortality from collisions with power lines is challenging due to the lack of studies, especially from sites within Canada, and due to uncertainty about the magnitude of detection biases. Detection of bird collisions with transmission lines varies due to habitat type, species size, and scavenging rates. In addition, birds can be crippled by the impact and subsequently die, although crippling rates are poorly known and rarely incorporated into estimates. We used existing data to derive a range of estimates of avian mortality associated with collisions with transmission lines in Canada by incorporating detection, scavenging, and crippling biases. There are 231,966 km of transmission lines across Canada, mostly in the boreal forest. Mortality estimates ranged from 1 million to 229.5 million birds per year, depending on the bias corrections applied. We consider our most realistic estimate, taking into account variation in risk across Canada, to range from 2.5 million to 25.6 million birds killed per year. Data from multiple studies across Canada and the northern U.S. indicate that the most vulnerable bird groups are (1) waterfowl, (2) grebes, (3) shorebirds, and (4) cranes, which is consistent with other studies. Populations of several groups that are vulnerable to collisions are increasing across Canada (e.g., waterfowl, raptors), which suggests that collision mortality, at current levels, is not limiting population growth. However, there may be impacts on other declining species, such as shorebirds and some species at risk, including Alberta’s Trumpeter Swans (Cygnus buccinator) and western Canada’s endangered Whooping Cranes (Grus americana). Collisions may be more common during migration, which underscores the need to understand impacts across the annual cycle. We emphasize that these estimates are preliminary, especially considering the absence of Canadian studies.

Alternative Model of Three-Phase Transmission Line Theory-Based Modal Decomposition

In this paper is shown the development of a transmission line, based on discrete circuit elements that provide responses directly in the time domain and phase. This model is valid for ideally transposed rows represent the phases of each of the small line segments are separated in their modes of propagation and the voltage and current are calculated at the modal field. However, the conversion phase-mode-phase is inserted in the state equations which describe the currents and voltages along the line of which there is no need to know the user of the model representation of the theory in the field lines modal.

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 Clarke's 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.

Applying a new methodology to verify transmission line model performance - the equivalent impedance test

The objective of this paper is to present a methodology to analyze a transmission line model used in electromagnetic transitory simulators, called equivalent impedance test. Initially the definition of equivalent impedance reference test is shown. Soon after this methodology is applied to a transmission line model, the Quasi-Modes model. The studies were accomplished in a hypothetical non-transposed three-phase transmission fine of 440 kV. The line length is 500 km, and it was modeled through cascades of pi-circuits (with 50 pi's circuits, each with 10 km length).

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, Clarke's matrix is used to separate the line into components a, 0, and zero. Because a 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 2 x 2 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 440 kV.

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.

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.