Efficient procedure to evaluate electromagnetic transients on three-phase transmission lines

This paper presents a hybrid way mixing time and frequency domain for transmission lines modelling. The proposed methodology handles steady fundamental signal mixed with fast and slow transients, including impulsive and oscillatory behaviour. A transmission line model is developed based on lumped elements representation and state-space techniques. The proposed methodology represents an easy and practical procedure to model a three-phase transmission line directly in time domain, without the explicit use of inverse transforms. The proposed methodology takes into account the frequency-dependent parameters of the line, considering the soil and skin effects. In order to include this effect in the state matrices, a fitting method is applied. Furthermore the accuracy of proposed the developed model is verified, in frequency domain, by a simple methodology based on line distributed parameters and transfer function related to the input/output signals of the lumped parameters representation. In addition, this article proposes the use of a fast and robust analytic integration procedure to solve the state equations, enabling transient and steady-state simulations. The results are compared with those obtained by the commercial software Microtran (EMTP), taking into account a three-phase transmission line, typical in the Brazilian transmission system.

Corona Discharge Model for Transmission Lines by Lumped Elements

This paper shows the insertion of corona effect in a transmission line model based on lumped elements. The development is performed considering a frequency-dependent line representation by cascade of pi sections and state equations. Hence, the detailed profile of currents and voltages along the line, described from a non-homogeneous system of differential equations, can be obtained directly in time domain applying numerical or analytic solution integration methods. The corona discharge model is also based on lumped elements and is implemented from the well-know Skilling-Umoto Model.

Analysis of the Electrical Characteristics of an Alternative Solution for the Brazilian-Amazon Transmission System

This article analyzes the electrical parameters of a 3-phase transmission line using a 280-m-high steel tower that has been proposed for the Amazon transmission system in Brazil. The height of the line conductors and the distance between them are intrinsically related to the longitudinal and transverse parameters of the line. Hence, an accurate study is carried out in order to show the electrical variations between a transmission line using the new technology and a conventional 3-phase 440-kV line, considering a wide range of frequencies and variable soil resistivity. First, a brief review of the fundamental theory of line parameters is presented. In addition, by using a digital line model, simulations are carried out in the time domain to analyze possible and critical over-voltage transients on the proposed line representation.

A procedure to estimate parameters of a line segment taking into account its representation through pi circuits: Theoretical development

The objective of this paper is to show an alternative methodology to estimate per unit length parameters of a line segment of a transmission line. With this methodology the line segment parameters can be obtained starting from the phase currents and -voltages in receiving and sending end of the line segment. If the line segment is represented as being one or more pi circuits whose frequency dependent parameters are considered lumped, its impedance and admittance can be easily expressed as functions of the currents and voltages at the sending and receiving end. Because we are supposing that voltages and currents at the sending and receiving end of the tine segment (in frequency domain) are known, it is possible to obtains its impedance and admittance and consequently its per unit length longitudinal and transversal parameters. The procedure will be applied to estimate the longitudinal and transversal parameters of a small segment of a single-phase line that is already built.

Application of pi Circuits for Simulation of Corona Effect in Transmission Lines

In this article, it is represented by state variables phase a transmission line which parameters are considered frequency independently and frequency dependent. Based on previous analyses, it is used the reasonable number of p circuits and the number of blocks composed by parallel resistor and inductor for reduction of numerical oscillations. It is analyzed the influence of the increase of the RL parallel blocks in the obtained results. The RL parallel blocks are used for inclusion of the frequency influence in the transmission line longitudinal parameter. It is a simple model that is been used by undergraduate students for simulation of traveling wave phenomena in transmission lines. Considering the model without frequency influence, it is included a representation of the corona effect. Some simulations are carried considering the corona effect and they are compared to the results without this phenomenon.

Non-transposed three-phase line analyses with a single real transformation matrix

In transmission line transient analyses, a single real transformation matrix can obtain exact modes when the analyzed line is transposed. For non-transposed lines, the results are not exact. In this paper, non-symmetrical and non transposed three-phase line samples are analyzed with a single real transformation matrix application (Clarke's matrix). Some interesting characteristics of this matrix application are: single, real, frequency independent, line parameter independent, identical for voltage and current determination. With Clarke's matrix use, mathematical simplifications are obtained and the developed model can be applied directly in programs based on time domain. This model works without convolution procedures to deal with phase-mode transformation. In EMTP programs, Clarke's matrix can be represented by ideal transformers and the frequency dependent line parameters can be represented by modified-circuits. With these representations, the electrical values at any line point can be accessed for phase domain or mode domain using the Clarke matrix or its inverse matrix. For symmetrical and non-transposed lines, the model originates quite small errors. In addition, the application of the proposed model to the non-symmetrical and non-transposed three phase transmission lines is investigated. ©2005 IEEE.

Allocation of the cost of transmission losses in a multimarket framework

The paper addresses the issue of apportioning of the cost of transmission losses to generators and demands in a multimarket framework. Line flows are unbundled using equivalent bilateral exchanges on a DC-network model and allocated to generators and demands. Losses are then calculated based on unbundled flows and straightforwardly apportioned to generators and demands. The proposed technique is particularly useful in a multimarket framework, where all markets have a common grid operator with complete knowledge of all network data, as is the case of the Brazilian electric-energy system. The methodology proposed is illustrated using the IEEE Reliability Test System and compared numerically with an alternative technique. Appropriate conclusions are drawn. © The Institution of Engineering and Technology 2006.

A procedure to estimate parameters of a line segment taking into account its representation through π circuits: Theoretical development

The objective of this paper is to show an alternative methodology to estimate per unit length parameters of a line segment of a transmission line. With this methodology the line segment parameters can be obtained starting from the phase currents and voltages in receiving and sending end of the line segment. If the line segment is represented as being one or more π circuits whose frequency dependent parameters are considered lumped, its impedance and admittance can be easily expressed as functions of the currents and voltages at the sending and receiving end. Because we are supposing that voltages and currents at the sending and receiving end of the line segment (in frequency domain) are known, it is possible to obtains its impedance and admittance and consequently its per unit length longitudinal and transversal parameters. The procedure will be applied to estimate the longitudinal and transversal parameters of a small segment of a single-phase line that is already built. © 2006 IEEE.

Modal representation of three-phase lines applying two transformation matrices: Evaluation of its eigenvectors

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 α, β 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. ©2006 IEEE.

Sensitivity analysis for overload-relief in transmission lines using an implicitly coupled method (CRIC)

The restructuring of energy markets to provide free access to the networks and the consequent increase of the number of power transactions has been causing congestions in transmission systems. As consequence, the networks suffer overloads in a more frequent way. One parameter that has strong influence on transfer capability is the reactive power flow. A sensitivity analysis can be used to find the best solution to minimize the reactive power flows and relief, the overload in one transmission line. The proposed methodology consists on the computation of two sensitivities based on the use of the Lc matrix from CRIC (Constant Reactive Implicitly Coupled) power flow method, that provide a set of actions to reduce the reactive power flow and alleviate overloads in the lines: (a) sensitivity between reactive power flow in lines and reactive power injections in the buses, (b) sensitivity between reactive power flow in lines and transformer's taps. © 2006 IEEE.

An alternative procedure to decrease the dimension of the frequency dependent modal transformation matrices: Application in three-phase transmission lines 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 α, β and zero. After that, Quasi-modes α 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. © 2006 IEEE.

Modelo AC para el despacho combinado de contratos bilaterales y bolsa de energía considerando restricciones de seguridad

Reliability is a key aspect in power system design and planning. Maintaining a reliable power system is a very important issue for their design and operation. Under the new competitive framework of the electricity sector, power systems find ever more and more strained to operate near their limits. Under this new scenario, it is crucial for the system operator to use tools that facilitate an energy dispatch that minimizes possible power cuts. This paper presents a mathematical model to calculate an energy dispatch that considers security constraints (single contingencies in transmission lines and transformers). The model involves pool markets and fixed bilateral contracts. Traditional methodologies that include security constraints are usually based in multistage dispatch processes. In this case, we propose a single-stage model that avoids the economic inefficiencies which result when conventional multi-stage dispatch approaches are applied. The proposed model includes an AC representation of the transport system and allows calculating the cost overruns incurred in due to reliability restrictions. We found that complying with fixed bilateral contracts, when they go above certain levels, might lead to congestion problems in transmission lines.

The use of current transformers for noise detection due to sparking in insulators strings in high voltage transmission lines

In a general way, in an electric power utility the current transformers (CT) are used to measurement and protection of transmission lines (TL) 1 The Power Line Carriers systems (PLC) are used for communication between electrical substations and transmission line protection. However, with the increasing use of optical fiber to communication (due mainly to its high data transmission rate and low signal-noise relation) this application loses potentiality. Therefore, other functions must be defined to equipments that are still in using, one of them is detecting faults (short-circuits) and transmission lines insulator strings damages 2. The purpose of this paper is to verify the possibility of using the path to the ground offered by the CTs instead of capacitive couplings / capacitive potential transformers to detect damaged insulators, since the current transformers are always present in all transmission lines (TL's) bays. To this a comparison between this new proposal and the PLC previous proposed system 2 is shown, evaluating the economical and technical points of view. ©2010 IEEE.

A First approach on the new transmission system in northern Brazil

This article shows an analysis of the electrical parameters of a three-phase transmission line section using a relatively new design for steel towers characterized by 280 meters high. These main features, the height of the line conductors and distance between them, are intrinsically related to the longitudinal and transversal parameters of the line. By this means, an analysis was carried out in order to show the electrical variations between a transmission line using the new technology and a conventional 440-kV line through a wide range of frequencies and a variable soil resistivity. © 2012 The Institution of Engineering and Technology.

Introduction of a non-conventional solution for Amazon transmission system: Analysis of the electric aspects

This article shows an analysis of the longitudinal electric parameters of a three-phase transmission line/section using a 280-meter high steel tower. This characteristic, the height of the line conductors and distance between them, are intrinsic related to the longitudinal and transversal parameters of the line. By this means, an accurate study was carried out in order to show the electric variations between a transmission line using the new technology and a three-phase conventional 440 kV line for a wide range of frequencies and a variable soil resistivity. In addition, by using a digital line model, simulations are carried out in time domain to analyze critical overvoltage transients on the studied line. © 2011 IEEE.