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Power transmission by cable is widely used in densely populated areas. Recently off-shore windfarms have become quite common, especially in Europe, and a number of off-shore windfarms are under construction and planned. Thus, a number of submarine cables have been installed and constructed. Submarine cables are also commonly used to connect an island to a mainland.
Further, in Denmark all the overhead lines above 100 kV are replaced by underground cables. Thus, transients in cable systems become a very important subject, especially in long and complex cable systems. The most significant difference of a cable from an overhead line is that a single-phase cable is composed of multi-conductors, that is, a core and a metallic sheath (shield), while a single overhead line is a single conductor. Thus, a three-phase cable (single-core coaxial cable) becomes a six conductor system. When the three-phase cable is enclosed in a conducting pipe, it becomes a seven conductor system.

Therefore, an analysis of cable voltages and currents necessitates a theory of multi-conductors. Another significant difference is that a cable is, in most cases, buried underground. This results in the propagation velocity of the earth-return mode along the cable being far smaller than that of an overhead line, which is nearly the velocity of light in free space. Also, the propagation velocity between a core and a metallic sheath (called “coaxial mode”) is determined by the relative permittivity 𝜀i of an insulator between the core and the sheath, which ranges from two to four, that is coaxial mode velocity cc = c0∕ √𝜀i, where c0 ≒ 300 m∕μs (velocity of light).
There are various types and kinds of cables: (1) a power transmission cable, a communication cable and a control/single cable; (2) a directly buried or tunnel installed underground cable, a submarine cable and an overhead cable such as a gas-insulated bus; (3) a single-core coaxial (SC) cable, a multi-core cable, and a pipe-enclosed type (PT) cable; (4) circular or cylindrical, and flat-shaped cables; (5) normal-bonded and cross-bonded cables.

This makes an analysis of cable voltages and currents far more complicated than that of an overhead line. As a matter of fact, the overhead line is categorized as just one of the cables, that is, a cable composed only of a core. This book deals with transients in a power system cable. In Chapter 1, various cables manufactured and used in practice are described. Chapter 2 explains the impedance and admittance formulas of typical cables, that is, an SC cable and a PT cable. Exact but complicated formulas for numerical calculations are described.
Also simple but approximate formulas for a hand calculation are explained so readers understand the physical meaning of the formulas. Most of the work in this book has been carried out at Doshisha University, Kyoto, Japan, and partially at the US Department of Energy, Bonneville Power Administration, Portland, OR, USA and at the Tokyo Electric Power Company, Tokyo, Japan. The authors are grateful for the provision of the necessary facilities and for the financial support they have received to carry out their work.