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.

Analyses of the modifications in the pi circuits for inclusion of frequency influence in transmission line representation

In this article, it is represented by state variables phase a transmission line which parameters are considered frequency independently and frequency dependent. It is analyzed what is the reasonable number of pi circuits and the number of blocks composed by parallel resistor and inductor in parallel for reduction of numerical oscillations. It is simulated the numerical routine with and without the effect of frequency in the longitudinal parameters. Initially, it is used state variables and pi circuits representing the transmission line composing a linear system which is solved by numerical routines based on the trapezoidal rule. The effect of frequency on the line is synthesized by resistors and inductors in parallel and this representation is analyzed in details. It is described transmission lines and the frequency influence in these lines through the state variables.

Integration Methods Used in Numerical Simulations of Electromagnetic Transients

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), Simpson's 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.

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

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

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.

Nuclear incoherent photoproduction of pi(0) and eta from 4 to 12 GeV

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

Phosphate distribution in the sediments along a cascade of reservoirs - (Paranapanema River, SE, Brazil)

Total phosphorus concentrations in the sediment of a cascade of 8 reservoirs located in the Paranapanema River (SE, Brazil) were analysed during two consecutive seasonal periods (2000 and 200 1). The reservoirs of Jurumirim, Chavantes, Salto Grande, Canoas 11, Canoas 1, Capivara, Taquarucu and Rosana were built during the last five decades with the purpose of hydroelectric generation. The sampling points were distributed along a 700 km of river stretch in 19 stations distributed in the river-reservoirs zones and main tributaries as well as in 5 stations representing the adjacent wetlands. The nutrient concentration was determined in samples from surface layers of sediment. Temporal and spatial changes were observed for both years. Three different areas could be identified along the river, considering not only Tot-P variations but also others physical and chemical characteristics such as organic matter concentration, nitrogen concentration of sediment and 02, pH, conductivity and Eh measured in the bottom layer of the water column. Higher values of Tot-P were found in the middle and lower region of the Paranapanema basin (maximum value of 1.96 mg g(-1) in Tibagi River in October/2001). Agricultural practices and cattle raising are the main external sources of nutrient in these regions. Superficial or sub-superficial watershed drainage and tributaries entrances are important nutrient contributors, leading to an increasing accumulation of nutrient in the sediment. This process seems to be especially important in the middle region of the Paranapanema Valley, were the values of Tot-P were higher comparing to the other areas.

Phytoplankton assemblages in a reservoir cascade of a large tropical - subtropical river (SE, Brazil)

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

Modified routine for decreasing numeric oscillations at associations of lumped elements

Some changes in the application of the numeric trapezoidal integration are analyzed for applications considering pi circuits. It is considered numeric and computational proceedings for improving the numeric results obtained with associations of pi circuits. In numeric integration solutions of the linear systems, it is common to represent these associations of pi circuits by only one matrix. This representation introduces undesirable numeric oscillations in simulations of the dynamics of wave propagation in electrical systems. The proposed changes improve the results of application of cascades of pi circuits associated to the trapezoidal integration, avoiding that the numerical oscillations, or Gibb's oscillations, have high values and are slowly damped. For the carried out simulations, different number of pi circuits and voltage sources are checked, confirming the reduction of the influence of the numeric oscillations on the obtained results. (C) 2014 Elsevier B.V. All rights reserved.

Reducing the spurious oscillations in the lumped parameters model using low-pass filter

Voltages and currents in the transmission line are described by differential equations that are difficult to solve due soil and skin effect that has to be considered for accurate results, but it increases their complexity. Therefore there are some models to study the voltages and currents along in transmission line. The distributed parameters model that transforms the equations in time domain to the frequency domain and once the solutions are obtained, they are converted to time domain using the Inverse Laplace Transform using numerical methods. Another model is named lumped parameters model and it considers the transmission line represented by a pi-circuit cascade and the currents and voltages are described by state equations. In the simulations using the lumped parameters model, it can be observed the presence of spurious oscillations that are independent of the quantity of pi-circuits used and do not represent the real value of the transient. In this work will be projected a passive low-pass filter directly inserted in the lumped parameters model to reduce the spurious oscillations in the simulations, making this model more accurate and reliable for studying the electromagnetic transients in power systems.

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.

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).

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.

Representation of transmission lines: comparison of models and parameters distributed discrete parameters

A transmission line is characterized by the fact that its parameters are distributed along its length. This fact makes the voltages and currents along the line to behave like waves and these are described by differential equations. In general, the differential equations mentioned are difficult to solve in the time domain, due to the convolution integral, but in the frequency domain these equations become simpler and their solutions are known. The transmission line can be represented by a cascade of π circuits. This model has the advantage of being developed directly in the time domain, but there is a need to apply numerical integration methods. In this work a comparison of the model that considers the fact that the parameters are distributed (Universal Line Model) and the fact that the parameters considered concentrated along the line (π circuit model) using the trapezoidal integration method, and Simpson's rule Runge-Kutta in a single-phase transmission line length of 100 km subjected to an operation power. © 2003-2012 IEEE.

Darunavir: A Critical Review of Its Properties, Use and Drug Interactions

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