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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Notes
- 1.
In reality, there is a small voltage in the screen.
- 2.
There are also dielectric losses that could be incorporated into the matrix, but they are small when compared with the capacitance.
- 3.
As we are dealing with matrices, the order of the matrices cannot be arbitrary.
- 4.
Numerically calculated for 20 kHz.
- 5.
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.
- 6.
It is not shown in Fig. 3.18b, but the coaxial sheath modes would eventually reach the velocity of the coaxial core modes.
- 7.
In this case the interarmour mode is compared with the intersheath mode.
- 8.
The differences between the two models are typically not very large up to the first resonance point, becoming more noticeable as the frequency increases.
- 9.
The variables a to g are real numbers that are used in the mathematical demonstration.
- 10.
Short circuits are special cases as we will see in Sect. 4.10.
- 11.
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.
- 12.
Assuming the system is lossless.
References and Further Reading
Popović Z, Popović BD (2000) Introductory electromagnetics. Prentice Hall, New Jersey
Greenwood A (1991) Electrical transients in power systems, 2nd edn. Wiley, New York
Marshall SV, Dubroff RE, Skitek GG (1996) Electromagnetic concepts and applications, 4th edn. Prentice Hall, New Jersey
Tleis N (2008) Power systems modelling and fault analysis: theory and practice. Elsevier, Oxford
Martinez-Velasco JA (2010) Power system transients: parameter determination. CRC Press, Boca Raton
van der Sluis L (2001) Transients in power systems. Wiley, New York
Dommel HW (1986) Electro-magnetic transients program (EMTP) theory book. Bonneville Power Administration, Portland
Wedepohl LM, Wilcox DJ (1973) Transient analysis of underground power-transmission systems: system-model and wave-propagation characteristics. In: Proceedings of the institution of electrical engineers, vol 120(2)
Brown GW, Rocamora RG (1976) Surge propagation in three-phase pipe-type cables, Part I: unsaturated pipe. IEEE Trans. Power Apparatus Syst PAS-95(1)
Ametani A (1980) Wave propagation characteristics of cables. IEEE Trans. Power Apparatus Syst PAS-99(2)
Ametani A (1980) A general formulation of impedance and admittance of cables. IEEE Trans. Power Apparatus Syst PAS-99(3)
Noualy JP, Le Roy G (1977) Wave-propagation modes on high-voltage cables. IEEE Trans. Power Apparatus Syst PAS-96(1)
Nagaoka N, Ametani A (1983) Transient calculations on crossbonded cables. IEEE Trans. Power Apparatus Syst PAS-102(4)
Morched A, Gustavsen B, Tartibi M (1999) A universal model for accurate calculation of electromagnetic transients on overhead lines and underground cables. IEEE Trans Power Delivery 14(3)
Yang Y, Ma J, Dawalibi FP (2001) Computation of cable parameters for pipe-type cables with arbitrary thicknesses. In: IEEE-PES transmission and distribution conference and exposition
Noda T (2008) Numerical techniques for accurate evaluation of overhead line and underground cable constants. IEEJ Trans Electr Electron Eng
Gudmundsdóttir US (2010) Modelling of long high voltage AC cables in transmission systems. PhD Thesis, Aalborg University
CIGRE WG B1.30 (2012) Cable systems electrical characteristics. CIGRE, Paris
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da Silva, F.F., Bak, C.L. (2013). Travelling Waves. In: Electromagnetic Transients in Power Cables. Power Systems. Springer, London. https://doi.org/10.1007/978-1-4471-5236-1_3
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DOI: https://doi.org/10.1007/978-1-4471-5236-1_3
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