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Additional information is available at the end of the chapter http://dx.doi.org/10.5772/48555 parameters in the models with frequency, the sum of the effect of soil, developed by Carson and Pollaczek, with skin effect, whose behavior as a function of frequency can be calculated using formulas derived from the Bessel equations.Models with variable parameters in terms of frequency are considered more accurate when compared to models that consider the constant parameters. The variation depends upon the frequency. This variation may be represented by series and parallel combination of resistive and inductive elements pure.As transmission lines are inserted in an electrical system that has many nonlinear elements and, thus, it is difficult to represent them in the frequency domain, there is a preference for line models that are developed directly in the time domain.Another factor, that makes the model lines developed directly in the time domain are most commonly used, is that the majority of programs that perform simulations electromagnetic transients in electrical systems require that the system components are represented in time domain.Probably, the first model to represent the transmission line directly in the time domain is designed for H. W. Dommel, which was based on the method of the characteristics or Bergeron's method. The model has combined the method of characteristics with the trapezoidal method numerical integration, resulting in an algorithm able to simulate transient electromagnetic networks whose parameters are distributed or discrete. This algorithm has undergone successive developments and is now known as the Electromagnetic Transients Program, or EMTP simply.In situations where one wants to simulate the propagation of electromagnetic waves resulting from operations carried out maneuvers and switching the transmission lines, it can be represented the same as a cascade of π circuits.In this model, each segment consists of a combination of series and parallel circuits composed by resistors and inductors. This results in an equivalent resistance and an inductance that depend on the frequency. It is considered in hese equivalent elements the ground and skin effects.Due to the fact that EMTP-type programs are not easy to use, several authors suggest describing the currents and voltages in the cascade of π circuits by means of state variables. The state equations are then transformed into differential equations and can be solved using any computer language or mathematical software.The representation of the line by means of state variables can be used in teaching basic concepts of wave propagation in transmission lines, the analysis of the distribution of currents and voltages along the line, and the simulation of electromagnetic transients in transmission lines with non-linear elements.Although the technique of state variables is widely used in the representation of transmission lines, it can be seen in recent publications, that it was only used to represent The MatLab TM Software Application for Electric...

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