Determination of the open-circuit sheath voltages of cable systems

The literature of the crossbonded a.c. cable systems is sparse and is mainly of Japanese and American origin. Recent work in the UK has indicated the need for precise numerical data on sheath conditions of these systems. The paper gives the numerical magnitudes of steady-state voltages and overvoltages to be expected on these systems, since they do not appear to have been formulated comprehensively in the literature. The sheath voltages can be found by identical methods for any cable system, whether it be transposed, crossbonded or normally laid. The system of calculation in the paper is thus part of a method for determining overall cable behaviour in terms of sheath voltages, currents and losses, and for either single or double circuits. Attention is drawn to the complexity of calculations for many modern systems with crossbonding, transposition and unequal lay lengths, from which it follows that more powerful mathematical methods, allied to fast large-store-capacity computers, become necessary. An economical system of notation, avoiding the use of multiple suffixes, is used, even though 3 × 3 × 3 × 2 × 2 variables must be permuted. Furthermore, in any lay (or section in the more complex cases) it is necessary to locate a particular sheath relative to a particular conductor, as well as locating each one geographically in the cable trench at any particular junction in a barrel of lays and sections. Results are presented for all the practical cases, together with single and double 3-phase circuits representing the theoretical limits. All results are given to the same base of induced voltages per 1000ft per 100A in the reference conductor; comparison of results is thus facilitated.