Admittance formulas

The latter approach does have its uses, however, particularly if one is interested in the sequence of multiple reflections in the sample which are, so to speak, concealed in the propagation factor f(Z) of admittance formulas. 

First, this book will illustrate a transient on a single-phase line from a physical viewpoint, and how it can be solved analytically by an electric circuit theory. The impedance and admittance formulas of an overhead line will also be described. Approximate formulas that can be computed using a pocket calculator will be explained to show that a transient can be analytically evaluated via hand calculation. Since a real power line contains three phases, a theory to deal with a multiphase line will be developed. Finally, the book describes how to tackle a real transient in a power system. A computer simulation tool is necessary for this— specifically the well-known simulation tool Electro Magnetic Transients Program (EMTP), originally developed by the U.S. Department of Energy, Bonneville Power Administration— which is briefly explained in Chapter 1. 

Theory of Distributed-Parameter Circuits and Impedance/Admittance Formulas... 

In this chapter, a theory of distributed-parameter circuits is explained starting from the approximate impedance and admittance formulas of an overhead conductor. The derivation of the approximate formulas is described from the viewpoint of the physical behavior of current and voltage on a conductor. 

To analyze a transient in a distributed-parameter line, a traveling-wave theory is explained for both single- and multiconductor systems. A method to introduce velocity difference and attenuation in the multiconductor system is described together with field test results. Impedance and admittance formulas of unusual conductors, such as finite-length and vertical conductors, are also explained. 

Wise derived an admittance formula considering an imperfecdy conducting earth in 1948 [12] ... 

This section explains impedance and admittance formulas of nonuniform lines, such as finite-length horizontal and vertical conductors based on a plane wave assumption. The formulas are applied to analyze a transient on a nonuniform line by an existing circuit theory-based simulation tool such as the EMTP [9,11]. The impedance formula is derived based on Neumann s inductance formula by applying the idea of complex penetration depth explained earlier. The admittance is obtained from the impedance assuming the wave propagation velocity is the same as the light velocity in free space in the same manner as an existing admittance formula, which is almost always used in steady-state and transient analyses on an overhead line. 

The penetration depth is physically defined as the depth for an electromagnetic wave penetrating into a conductor when the wave hits the conductor surface. The physical concept of the penetration depth is very useful to explain the behavior of a current and a voltage on a conductor and also to derive impedance and admittance formulas of various conductor shapes and geometrical configuration. However, it should be reminded that the concept is based on TEM wave propagation and thus is not applicable to non-TEM propagation. Also, remind that it is just an approximation. 

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