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2013 | OriginalPaper | Buchkapitel

3. Travelling Waves

verfasst von : Filipe Faria da Silva, Claus Leth Bak

Erschienen in: Electromagnetic Transients in Power Cables

Verlag: Springer London

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Abstract

“Travelling Waves and Modal Domain”, reviews the Telegraph equations and how to calculate the loop and series impedance matrices as well as the shunt admittance matrix of a cable in function of the frequency. The chapter also introduces the different modes of a cable, how to calculate their impedance and velocity as well as their frequency dependence. The knowledge of modal theory is of outmost importance when working in transient in cables. It is true that in many cases, software is used to run simulations, and the reader may be tempted to think that only those designing the software need to know how to use modal theory. However, several phenomena require at least a minimum knowledge of the topic and for that reason; the book provides a thorough explanation of the subject. This chapter also studies the frequency spectrum of a cable for different modelling configurations, introducing the power of lower resonance frequencies.

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Vorheriges Kapitel Simple Switching Transients

Nächstes Kapitel Transient Phenomena

In reality, there is a small voltage in the screen.

There are also dielectric losses that could be incorporated into the matrix, but they are small when compared with the capacitance.

As we are dealing with matrices, the order of the matrices cannot be arbitrary.

Numerically calculated for 20 kHz.

This does not mean that the screen impedance decreases with the frequency. It means that when compared with the other impedances it is relatively lower for high frequencies.

It is not shown in Fig. 3.18b, but the coaxial sheath modes would eventually reach the velocity of the coaxial core modes.

In this case the interarmour mode is compared with the intersheath mode.

The differences between the two models are typically not very large up to the first resonance point, becoming more noticeable as the frequency increases.

The variables a to g are real numbers that are used in the mathematical demonstration.

Short circuits are special cases as we will see in Sect. 4.10.

The opposite case happens for a quarter wavelength, which corresponds to very low impedances. If the line is short circuited in the end the opposite occurs, very high impedance at a quarter wavelength and very low at half wavelength.

Assuming the system is lossless.

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Titel: Travelling Waves
verfasst von: Filipe Faria da Silva
Claus Leth Bak
Verlag: Springer London
Buch: Electromagnetic Transients in Power Cables
Print ISBN: 978-1-4471-5235-4

Electronic ISBN: 978-1-4471-5236-1

Copyright-Jahr: 2013
DOI: https://doi.org/10.1007/978-1-4471-5236-1_3