Cable Geometry Research Articles

Computer solution of e.h.v. underground-cable cooling problems

Resistance-network analogues have been used experimentally for longitudinal step-by-step solution of the thermal problem in separate-water-pipe cooling of underground e.h.v. cables. In parallel with this technique, mathematical models have been programmed for digital and analogue computers. The feature of the digital solution is the use of two programs; the first need only be run once, giving results which are applicable as boundary conditions to various cable and pipe geometries in the second program, in which both radial and square meshes are used. The analogue program in which the digital results are used is simple, versatile and suitable for general application to most cable geometries. The derivations of the thermal equations and the development of the computer programs are given in detail, and results for typical cable systems are presented.

789. Instability of refractory metal thermocouples: B E Walker et al, US Govt Res Develop Repts, 40 (21), 5 NOV 1965, AD-621 484, 18 pages

A simple generic cryostat thermal model has been developed for the purpose of predicting cryogen mass and lifetime of cryogenic space telescopes. The model was created for use with the Martin Marietta thermal analyser, mini-MITAS, on microcomputers. The model is based on a lumped parameter representation of eight nodes and over 35 conductors. The major telescope dewar components represented as nodes are the main cryogen tank, the three vapour-cooled shields, the outer shell, barrel baffle and the barrel baffle heat exchanger. The input to the model consists of the vapour-cooled shield, support straps and instrument cable geometry and the cryostat heat loads from the instrument and through the aperture. The outer shell and superfluid helium temperatures are assumed to be known. The predictions from the model were compared with those from the more detailed models of IRAS, COBE and SIRTF. Correlation of the helium flow rates of the IRAS and COBE Dewars was 12% above the actual flight or ground test data and for SIRTF it was less than 2% of the prediction from the detailed model. Currently, this model is being used for the conceptual design studies of the Submillimetre Imager and Line Survey (SMILS) telescope.

Discussion at annual convention: Cable charge and discharge: Dielectric strength ratio between alternating and direct voltages: Cable geometry and the calculation of current carrying capacity

J. B. Whitehead: The approximate exponential shape of the charge and discharge curves of composite dielectrics has long been recognized, and many efforts have been made to explain the departure of these curves from the pure exponential form, by various assumptions as to the structure of the dielectric in various arrangements of high resistance paths in conjunction with capacities. Several of these suggestions are in approximate conformity to the experimental observations of the charge and discharge curves as observed with continuous potentials. One of the simplest of all is that used by Dr. Steinmetz in which assumption is made of a very high resistance in series with a capacity, a number of such combinations being assumed with different relative values of the resistances and capacities. Another recent analysis of the problem has been given by K. W. Wagner who, with an entirely different method of approach, through a modification of Maxwell's suggestion of a mixture of two or more dielectrics, reaches the same conclusion as does Dr. Steinmetz, namely that the charge and discharge curves have one principal exponential term accompanied by one or more additional terms of relatively much smaller magnitudes.

Cable geometry and the calculation of current-carrying capacity

Cable geometry and the calculation of current-carrying capacity

Cable Geometry and the Calculation of Current-Carrying Capacity

The main purpose of this article is to express the calculation of current-carrying capacity in simple formulas. The allowable current for underground cables is usually limited by the maximum permissible temperature of the insulation. The temperature rise is of course a function of the ability of the cable system to dissipate the heat generated. The chief difficulty in the calculation of current-carrying capacity is the determination of the thermal resistances of the path through which the heat must flow. The main part of this paper deals with the errors in the standard formulas for calculating the thermal resistance and geometric properties between the conductors and the sheath. A graphical method of correcting the errors is obtained in terms of what is called the “geometric factor,” the results are tabulated for 2, 3 and 4-conductor cables throughout the range of practical sizes and an empirical formula is given. The check between the results of the graphical correction method and the published experimental data on this subject is very satisfactory, and emphasizes the errors in the standard formulas. The thermal resistance between the sheath and the duct is mentioned briefly, and an approximate method of finding the resistance between the duct and the region at base temperature is outlined. The previous work is then combined into a simple formula giving the allowable current for n-conductor cables, there being any number of similar cables in the duct bank. The formula is also enlarged to cover the case of cables in the metric and square inch systems, and cables buried directly in the ground. The method of including the effect of induced sheath currents in single-conductor cables and of dielectric losses is shown. Finally, the procedure to use in case the cables in the duct bank are not all of the same type is outlined. In Appendix A the geometric factor for three-conductor cables under three-phase voltage is discussed, Russell's formula for this geometric factor being compared with the experimental determinations and an empirical formula for it is given. A formula is also given for the calculation of dielectric losses in three-conductor cables. The geometric factors for three-conductor cables in all other connections (i. e., the geometric factor for one conductor against the other two and sheath, or between any two conductors, etc.) are then derived in terms of the two geometric factors already obtained. In Appendix B are given examples of the calculation of current carrying capacity under various conditions, and of dielectric loss. In Appendix C an example is given which shows the error introduced by using an approximate formula for the calculation of the thermal resistivity of the insulation of a three-conductor cable based upon experimental measurements, the case taken up being a table in the Research on the Heating of Buried Cables.

On the failure to lay the submarine cable

This paper presents the formulation and solution of governing equations that can be used to analyse the three-dimensional (3D) behaviour of either marine cables during installation or the response of segmented elastic mooring line catenaries as used for floating offshore structures when both are subjected to arbitrary sheared currents. The methodology used is an extension of one recently developed for analyses of marine cables when being installed on the seabed or being towed. The formulation describes elastic cable geometry in terms of two angles, elevation and azimuth, which are related to Cartesian co-ordinates by geometric compatibility relations. These relations are combined with the cable equilibrium equations to obtain a system of non-linear differential equations, which are numerically integrated by fourth and fifth order Runga–Kutta methods. The inclusion of cable elasticity and the ability to consider arbitrary stored currents are key features of this analysis. Results for cable tension, angles, geometry and elongation are presented for three example cases—the installation of a fibre optic marine cable, the static analysis of a deep water mooring line and the response of a telecommunications cable to a multi-directional current profile.